A method and system for estimating the frequency of an audio sinusoidal signal based on DFT

Abstract

The present invention discloses a method and system for estimating the frequency of an audio sinusoidal signal based on a DFT. The method comprises the following steps: first, performing a peak search on the signal's DFT amplitude spectrum to obtain the index value corresponding to the peak spectral line and obtain a rough frequency estimate; then, by interpolating the left and right spectral lines of the peak spectral line, as well as the left and right half spectral lines, the deviation δ of the rough frequency estimate is calculated to obtain the complete signal frequency. The method can effectively suppress white noise, has high estimation accuracy and noise immunity, and can resolve the technical problem of the prior art, which is the conflict between algorithm complexity and algorithm estimation accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of signal processing and communication technology, and in particular relates to a method and system for estimating the frequency of an audio sinusoidal signal based on DFT (Discrete Fourier Transform). Background Art

[0002] The frequency estimation problem of sinusoidal signals in a noisy background is an important research topic in the field of digital signal processing. With the development of information technology, it has been widely used in many engineering fields such as mobile communications, radar, audio and video. Among them, audio signals are a typical signal type that is suitable for description using the sinusoidal signal model.

[0003] Numerous sinusoidal signal frequency estimation methods have been proposed in numerous domestic and international literature. Based on the signal characteristics used, existing estimation schemes can be categorized into two main categories: time-domain and frequency-domain. Algorithms for estimating sinusoidal frequency parameters based on time-domain characteristics primarily include maximum likelihood estimation, autocorrelation, and linear prediction. Sinusoidal signal estimation algorithms based on frequency-domain characteristics typically first perform a discrete Fourier transform on the observed sampled signal and then extract parameters such as frequency based on the signal's spectral characteristics.

[0004] Due to its many advantages, such as simple implementation and high computational efficiency, the DFT estimator has become a widely used and widely explored method in the field of sinusoidal signal frequency estimation. However, its inherent flaws, such as spectrum leakage and picket fence effects in incoherent sampling environments, can affect the estimator's accuracy. Improved DFT-based frequency estimation algorithms, such as windowing and interpolation, can improve the accuracy of DFT frequency estimators to a certain extent. To further enhance estimation accuracy, iterative DFT algorithms have been proposed. However, the introduction of iterations generates additional computational effort, resulting in a significant computational burden and limiting the algorithm's real-time processing capabilities. Summary of the Invention

[0005] The present invention aims to provide a method and system for estimating the frequency of an audio sinusoidal signal based on DFT to address one or more of the above-mentioned technical problems. The technical solution provided by the present invention can solve the technical problem of the contradiction between algorithm complexity and algorithm estimation accuracy in the above-mentioned prior art.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] The present invention provides a method for estimating the frequency of an audio sinusoidal signal based on DFT, comprising the following steps:

[0008] Collect the single-tone audio sinusoidal signal to be processed and obtain the observation signal sequence of N sample points; the sampling result in a noise-free environment is represented as a signal waveform A, f and Represent the amplitude, frequency and phase of the sinusoidal signal respectively, n = 0, 1, ..., N-1 is the discrete signal index, Expressed as v is the digital frequency of the signal, p∈{0, 1, …, N-1}, |δ|≤0.5 are the integer part frequency and fractional part frequency of the digital frequency v respectively;

[0009] Perform N-point discrete Fourier transform on the observed signal sequence of the N sample points to obtain the transformed signal DFT spectrum line sequence X[k], which is expressed as:

[0010] Where k = 0, 1, ..., N-1 is the DFT coefficient index; i is the imaginary number symbol;

[0011] Search the signal DFT spectrum line sequence X[k] to locate the spectrum line with the largest amplitude as the peak spectrum line X[p], and use the index value of the peak spectrum line X[p] as the estimated value of the integer part frequency p;

[0012] Calculate the value of the interpolated spectrum line X[p±0.5] of half the index in the left and right directions of the peak spectrum line X[p], and determine the spectrum line used for estimation based on the calculated spectrum line value; calculate the fractional frequency based on the spectrum line used for estimation determined by the judgment estimated value of;

[0013] Combine the estimated value of the integer part frequency p and the fractional part frequency The estimated value of the digital angular frequency is obtained Complete the frequency estimation of the audio sinusoidal signal.

[0014] A further improvement of the method of the present invention is that the value of the interpolated spectrum line X[p±0.5] of the half index in the left and right directions of the peak spectrum line X[p] is calculated, and the spectrum line used for estimation is determined based on the spectrum line value obtained by calculation; based on the spectrum line used for estimation determined by judgment, the fractional frequency is calculated. The steps for estimating the value include:

[0015] When X[p-1]>X[p+0.5], X[p-1], X[p-0.5] and X[p] are the three largest DFT coefficients. At this time, X[p-1] and X[p] are used to obtain the estimated value of δ. The calculation expression is

[0016] When X[p + 1] > X[p - 0.5], X[p + 1], X[p + 0.5] and X[p] are the three largest DFT coefficients. At this time, X[p + 1] and X[p] are used to obtain an estimated value of δ, and the calculation expression is

[0017] In other cases, X[p - 0.5], X[p + 0.5] and X[p] are the three largest DFT coefficients. At this time, X[p + 0.5] and X[p - 0.5] are used to obtain an estimated value of δ, and the expression is

[0018] A further improvement of the method of the present invention is that the values of the interpolation spectra X[p ± 0.5] of half an index in the left and right directions of the peak spectrum line X[p] are calculated, and the spectra used for estimation are determined based on the calculated spectrum values; based on the spectra used for estimation determined by the judgment, the fractional part frequency ​​​​​​​​​​​​​​​​​​​​​​​​​​​​When X[p - 0.5] < X[p + 0.5], if At this time, X[p + 1] and X[p] are used to obtain an estimated value of δ, and the calculation expression is If At this time, X[p - 0.5] and X[p + 0.5] are used to obtain an estimated value of δ, and the calculation expression is In other cases, at this time, X[p + 0.5] and X[p] are used to obtain an estimated value of δ, and the calculation expression is

[0024] An audio sine signal frequency estimation system based on DFT provided by the present invention includes:

[0025] An observation signal sequence acquisition module, configured to collect a single-tone audio sine signal to be processed and obtain an observation signal sequence of N sample points; wherein, the sampling result in a noise-free environment is represented as a signal waveform A, f, and respectively represent the amplitude, frequency, and phase of the sine signal, n = 0, 1,..., N - 1 is a discrete signal index, is represented as v is the digital frequency of the signal, p ∈ {0, 1,..., N - 1}, |δ| ≤ 0.5 are respectively the integer part frequency and the fractional part frequency of the digital frequency v;

[0026] An integer part frequency estimation value acquisition module, configured to perform an N-point discrete Fourier transform on the observation signal sequence of the N sample points to obtain a transformed signal DFT spectral line sequence X[k], and the expression is In the formula, k = 0, 1,..., N - 1 is a DFT coefficient index; i is an imaginary symbol; search the signal DFT spectral line sequence X[k] to locate the spectral line with the largest amplitude as the peak spectral line X[p], and use the index value of the peak spectral line X[p] as the estimated value of the integer part frequency p;

[0027] A fractional part frequency estimation value acquisition module, configured to calculate the values of the interpolation spectral lines X[p ± 0.5] in half an index in the left and right directions of the peak spectral line X[p], determine the spectral line used for estimation based on the calculated spectral line values; based on the determined spectral line used for estimation, calculate and obtain the fractional part frequency of the estimated value;

[0028] An estimation result acquisition module, configured to combine the estimated value of the integer part frequency p and the fractional part frequency of the estimated value to obtain an estimated result of the digital angular frequency Complete the audio sine signal frequency estimation.

[0029] A further improvement of the system of the present invention is that the values of the interpolated spectra X[p±0.5] in the left and right half-index directions of the peak spectrum line X[p] are calculated, and the spectrum used for estimation is determined based on the calculated spectrum values; based on the spectrum used for estimation determined by the judgment, the fractional part frequency is calculated The steps for obtaining the estimated value of

[0030] When X[p - 1] > X[p + 0.5], X[p - 1], X[p - 0.5] and X[p] are the three largest DFT coefficients. At this time, X[p - 1] and X[p] are used to obtain the estimated value of δ, and the calculation expression is

[0031] When X[p + 1] > X[p - 0.5], X[p + 1], X[p + 0.5] and X[p] are the three largest DFT coefficients. At this time, X[p + 1] and X[p] are used to obtain the estimated value of δ, and the calculation expression is

[0032] In other cases, X[p - 0.5], X[p + 0.5] and X[p] are the three largest DFT coefficients. At this time, X[p + 0.5] and X[p - 0.5] are used to obtain the estimated value of δ, and the expression is [[ID=1​​​​​​​​​​​​​​​ The steps for estimating the value specifically include:

[0037] When X[p - 0.5] > X[p + 0.5], if At this time, X[p - 1] and X[p] are used to obtain the estimated value of δ, and the calculation expression is If At this time, X[p - 0.5] and X[p + 0.5] are used to obtain the estimated value of δ, and the calculation expression is In other cases, X[p - 0.5] and X[p] are used to obtain the estimated value of δ, and the calculation expression is

[0038] When X[p - 0.5] < X[p + 0.5], if At this time, X[p + 1] and X[p] are used to obtain the estimated value of δ, and the calculation expression is If At this time, X[p - 0.5] and X[p + 0.5] are used to obtain the estimated value of δ, and the calculation expression is In other cases, at this time, X[p + 0.5] and X[p] are used to obtain the estimated value of δ, and the calculation expression is

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] The present invention provides a method for estimating the frequency of a single - tone sine signal based on interpolated DFT. First, by performing a spectral peak search on the DFT amplitude spectrum of the signal, the index value corresponding to the peak spectral line is obtained to obtain a rough frequency estimation result; then, through interpolation of the spectral lines on both sides of the peak spectral line and the left and right half spectral lines, the deviation δ of the rough frequency estimation value is calculated to obtain the complete signal frequency. This method can effectively suppress white noise and has high estimation accuracy and anti - noise performance. Specifically, the present invention selects and uses the DFT coefficient with a larger amplitude through judgment, which can make the result estimated by the estimator more accurate when the signal is affected by noise interference; in addition, the present invention uses polynomial fitting to realize the utilization of DFT coefficient combinations that cannot be utilized through formulas; furthermore, the present invention combines and complements two algorithms, and can highly improve the estimation accuracy without increasing the computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following briefly introduces the drawings required for description in the embodiments or the prior art; obviously, the drawings in the following description are some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0042] Figure 1 1 is a flow chart of a method for estimating the frequency of an audio sinusoidal signal based on DFT according to an embodiment of the present invention;

[0043] Figure 2 Schematic diagram of the relationship between the DFT coefficients and DTFT transform of a single-tone sinusoidal signal;

[0044] Figure 3 1 is a schematic diagram of the mean square error of the algorithm according to the embodiment of the present invention at different fractional frequencies when the signal-to-noise ratio is 0 dB;

[0045] Figure 4 1 is a schematic diagram of the mean square error of the algorithm according to the embodiment of the present invention at different fractional frequencies when the signal-to-noise ratio is 40 dB;

[0046] Figure 5 It is a flowchart of the calculation steps of the algorithm of the embodiment of the present invention;

[0047] Figure 6 The figure is a schematic diagram of the mean square error of the algorithm according to the embodiment of the present invention under different signal-to-noise ratio conditions for a single-tone audio signal. DETAILED DESCRIPTION

[0048] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0049] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0050] The present invention is described in further detail below with reference to the accompanying drawings:

[0051] See also Figure 1, an embodiment of the present invention provides a sinusoidal signal frequency estimation method based on DFT, comprising the following steps:

[0052] Step 1: Collect the single-tone audio sinusoidal signal to be processed. The sampling result in a noise-free environment is the signal waveform Where A, f and Represent the amplitude, frequency and phase of the sinusoidal signal respectively, n = 0, 1, ..., N-1 is the discrete signal index; for the observation signal sequence of N sample points, It can be expressed as Where v is the digital frequency of the signal, p∈{0, 1, …, N-1} and |δ|≤0.5 are the integer and fractional parts of the digital frequency v respectively;

[0053] Step 2: First, perform N-point discrete Fourier transform on the N-point sine sequence collected above to obtain the transformed spectrum X[k].

[0054]

[0055] Where k = 0, 1, ..., N-1 is the DFT coefficient index; i is the imaginary number symbol;

[0056] Step 3: Search the signal DFT spectrum line sequence X[k] to locate the spectrum line with the maximum amplitude and obtain a rough estimate of the system frequency, that is, obtain an estimate of the integer part frequency p;

[0057] Step 4: Calculate the value of the interpolation point X[p±0.5] of half the index in the left and right directions of the peak spectrum line X[p];

[0058] Step 5: Use judgment to determine the points to use for the estimate, and then calculate the fractional part of the estimate Combined with the estimated value of the integer part frequency, the estimated result of the digital angular frequency can be finally obtained.

[0059] Calculating the estimated value of the decimal part based on the judgment in step 5 includes the following steps:

[0060] Step 5.1: When X[p-0.5]>X[p+0.5], if At this time, use X[p-1] and X[p] to obtain the estimated value of δ, that is,

[0061] Step 5.2: If At this time, use X[p-0.5] and X[p+0.5] to obtain the estimated value of δ, that is,

[0062] Step 5.3: In other cases when X[p - 0.5] > X[p + 0.5], at this time, use X[p - 0.5] and X[p] to obtain an estimated value of δ, that is

[0063] Step 5.4: When X[p - 0.5] < X[p + 0.5], if At this time, use X[p + 1] and X[p] to obtain an estimated value of δ, that is

[0064] Step 5.5: If At this time, use X[p - 0.5] and X[p + 0.5] to obtain an estimated value of δ, that is

[0065] Step 5.6: In other cases, at this time, use X[p + 0.5] and X[p] to obtain an estimated value of δ, that is

[0066] Finally, add the rough estimated value to obtain the final frequency

[0067] The embodiment of the present invention discloses a method for estimating the frequency of a sine signal based on DFT, which is applicable to the frequency estimation problem in an audio system. Currently, there are many frequency estimation algorithms based on the DFT domain, which can be mainly divided into two categories: iterative and non-iterative. Among them, most of the existing non-iterative methods have very low complexity, but it is difficult to achieve very satisfactory estimation accuracy. The iterative DFT algorithm greatly improves the estimation accuracy. However, the introduction of iteration will generate additional computational complexity. To solve this problem, an IpDFT algorithm based on adjacent spectral lines of the signal is proposed. The present invention first performs a discrete Fourier transform on the time-domain signal, and obtains the index value corresponding to the peak spectral line by searching the DFT magnitude spectrum, that is, the rough estimated value p of the frequency; then, through interpolation of the left and right spectral lines and the left and right half spectral lines of the peak spectral line, calculate the deviation δ of the rough estimated value of the frequency, so as to obtain the complete signal frequency. The method of the embodiment of the present invention can effectively suppress white noise and has high estimation accuracy and anti-noise performance.

[0068] Please refer to Figures 2 to 6 , a method for estimating the frequency of a sine signal based on DFT according to an embodiment of the present invention, includes:

[0069] In a noise-free environment, the waveform x[n] of a single-tone audio sine signal can be represented in discrete time form as where A, f and respectively represent the amplitude, frequency and phase of the sine signal, f S represents the sampling frequency, and n = 0, 1,..., N - 1 is the discrete signal index. For the observed signal sequence of N sample points, It can be expressed as Where v is the digital frequency of the signal, p∈{0, 1,…, N-1} and |δ|≤0.5 are the integer and fractional parts of the digital frequency v, respectively.

[0070] The following embodiments of the present invention discuss how to use an interpolation DFT algorithm to estimate the frequency v of a sinusoidal signal, including: first, performing an N-point discrete Fourier transform on the N-point sine sequence collected above to obtain the transformed spectrum X[k]. Based on the spectral line sequence after the DFT transform, an estimate of the frequency p of the integer part of the signal is obtained, that is, a rough estimate of the system frequency, which is the index represented by the spectral line with the largest DFT coefficient. Based on the characteristics of the DFT, it can be seen that the DFT transform of a complex sinusoidal signal is obtained by shifting the DTFT transform result of a rectangular window of length N on the spectrum and then sampling it. Figure 2 This shows the relationship between DTFT and DFT. It can be seen that the spectrum has a large main lobe and many other side lobes. Among them, the amplitude of the main lobe is much larger than that of the side lobes. For a DFT spectrum containing noise, using DFT coefficients with larger amplitudes to estimate the frequency can achieve better resistance to noise interference. This is because for coefficients with larger amplitudes, when subjected to noise interference, the amplitude of their amplitude change is smaller than that of coefficients with smaller amplitudes, so they have stronger resistance to noise interference. Therefore, the embodiment of the present invention chooses to obtain the DFT coefficients used to calculate the deviation δ of the rough frequency estimate by comparing the peak spectrum line X[p], the left and right spectrum lines X[p-1] and X[p+1], and the interpolation values ​​X[p-0.5] and X[p+0.5] of the left and right half spectrum lines, thereby obtaining the complete signal frequency.

[0071] In the embodiment of the present invention, the three points with the largest amplitude among the above five points are obtained. Figure 2 It can be seen that when X[p-1]>X[p+0.5], X[p-1], X[p-0.5], and X[p] are the three largest DFT coefficients. At this time, X[p-1] and X[p] are used to obtain the estimated value of δ, and the expression is

[0072] When X[p+1]>X[p-0.5], X[p+1], X[p+0.5], and X[p] are the three largest DFT coefficients. At this time, X[p+1] and X[p] are used to obtain the estimated value of δ, which is expressed as

[0073] In other cases, X[p-0.5], X[p+0.5], and X[p] are the three largest DFT coefficients. In this case, X[p+0.5] and X[p-0.5] are used to obtain the estimated value of δ, which is expressed as

[0074] Finally, the rough estimate value is added to obtain the final frequency

[0075] In the above method, the largest DFT coefficient is not used for estimation. This is because if the largest and the second-largest coefficients are used, it is impossible to obtain the estimated value of δ through these two coefficients using an analytical expression. The expression is

[0076]

[0077] However, the ratio of these two coefficients and δ are in one-to-one correspondence, and their functional relationship is monotonic. Therefore, the polynomial fitting method is adopted to describe the relationship between δ and In the embodiments of the present invention, creatively, in order to obtain a lower estimator system bias, it is decided to use a ninth-order polynomial for fitting, and the fitting polynomial result is represented by For the relationship between δ and It can be seen from the formula that

[0078] When X[p - 0.5] > X[p + 0.5], X[p - 0.5] and X[p] are the two largest DFT coefficients. At this time, X[p - 0.5] and X[p] are used to obtain the estimated value of δ, and the expression is

[0079] When X[p - 0.5] < X[p + 0.5], X[p + 0.5] and X[p] are the two largest DFT coefficients. At this time, X[p + 0.5] and X[p] are used to obtain the estimated value of δ, and the expression is

[0080] Finally, the rough estimate value is added to obtain the final frequency

[0081] In the embodiments of the present invention, for the purpose of exploring the performance of the algorithm proposed in the embodiments of the present invention, the signal is modeled and the accuracies of the two algorithms are compared. The signal amplitude A = 1 selected in the present invention, the phase takes any value, the number of observed sample points N = 2048, and the sampling frequency f <000oooo2> is 44100Hz. This signal is a typical high-pitched single-tone audio signal. In order to better evaluate the frequency estimation performance of the method of the present invention, the Cramer-Rao lower bound (CRLB) is introduced as a reference. CRLB represents the lowest value that the mean square error of signal parameter estimation can reach, that is, the best performance limit of the estimation algorithm. For the complex sine signal model used in the present invention, the calculation formula of its frequency estimation CRLB is as follows:

[0082] Where \(N\) is the number of samples of the observed signal, and \(\rho\) represents the signal-to-noise ratio of the sine signal. In this set of simulations, for the given signal, the frequency estimation results of these two algorithms are given when the signal-to-noise ratio is \(0\ dB\) and \(40\ dB\), and \(\delta\) increases from \(-0.5\) to \(0.5\) with a step size of \(0.05\). Figure 3 The simulation results for a signal-to-noise ratio of \(0\ dB\) Figure 4 The simulation results of the algorithm for a signal-to-noise ratio of \(40\ dB\). Here, analytic represents the first proposed algorithm, and fitting represents the second algorithm. It can be observed that for different values of \(\delta\), the estimation accuracies of these two algorithms have their own advantages and disadvantages. When \(0.1\lt|\delta|\lt0.4\), the second algorithm has higher estimation accuracy; in other cases, the first algorithm is more accurate.

[0083] In order to better improve the performance, the present invention combines the above two algorithms and proposes a joint algorithm, which has very high estimation accuracy and is better than all current non-iterative DFT domain algorithms. The specific steps are as follows:

[0084] When \(X[p - 0.5]\gt X[p + 0.5]\), if At this time, \(X[p - 1]\) and \(X[p]\) are used to obtain the estimated value of \(\delta\), and the expression is

[0085] If At this time, \(X[p - 0.5]\) and \(X[p + 0.5]\) are used to obtain the estimated value of \(\delta\), and the expression is

[0086] In other cases, at this time \(X[p - 0.5]\) and \(X[p]\) are used to obtain the estimated value of \(\delta\), and the expression is

[0087] When \(X[p - 0.5]\lt X[p + 0.5]\), if At this time, \(X[p + 1]\) and \(X[p]\) are used to obtain the estimated value of \(\delta\), and the expression is

[0088] If At this time, \(X[p - 0.5]\) and \(X[p + 0.5]\) are used to obtain the estimated value of \(\delta\), and the expression is

[0089] In other cases, we use \(X[p + 0.5]\) and \(X[p]\) to obtain the estimated value of \(\delta\) at this time, and the expression is

[0090] Finally, the rough estimated value is added to obtain the final frequency The final algorithm steps are as Figure 5 shown.

[0091] In combination with the above embodiments, in order to further analyze the noise resistance performance of the method proposed in the present invention, the single-tone audio signal as mentioned above is used to observe the frequency estimation performance of the proposed algorithm as the signal-to-noise ratio SNR changes, as shown in FIG. Figure 6 As shown, the frequency estimation mean square error of the combined algorithm proposed in the present invention shows an approximately linear downward trend with the increase of the signal-to-noise ratio, and the estimation accuracy of the algorithm improves with the increase of the signal-to-noise ratio; and in the case of most signal-to-noise ratios, the combined algorithm proposed in the present invention always has the smallest mean square error and the highest estimation accuracy among the current non-iterative algorithms. In summary, the frequency estimation method of a single-tone sinusoidal signal based on interpolation DFT proposed in the present invention has excellent performance and effectively suppresses the influence of white noise. It has the characteristics of simple calculation, high estimation accuracy and strong noise resistance.

[0092] The following are device embodiments of the present invention, which can be used to perform the method embodiments of the present invention. For details not disclosed in the device embodiments, please refer to the method embodiments of the present invention.

[0093] In another embodiment of the present invention, a DFT-based audio sinusoidal signal frequency estimation system is provided, comprising:

[0094] The observation signal sequence acquisition module is used to collect the single-tone audio sinusoidal signal to be processed and obtain the observation signal sequence of N sample points; the sampling result in a noise-free environment is represented as a signal waveform A, f and Represent the amplitude, frequency and phase of the sinusoidal signal respectively, n = 0, 1, ..., N-1 is the discrete signal index, Expressed as v is the digital frequency of the signal, p∈{0, 1, …, N-1}, |δ|≤0.5 are the integer part frequency and fractional part frequency of the digital frequency v respectively;

[0095] The integer part frequency estimation value acquisition module is used to perform N-point discrete Fourier transform on the observed signal sequence of the N sample points to obtain the transformed signal DFT spectrum line sequence X[k], which is expressed as follows: Wherein, k=0, 1, ..., N-1 is the DFT coefficient index; i is the imaginary number symbol; searching the signal DFT spectrum line sequence X[k] to locate the spectrum line with the largest amplitude as the peak spectrum line X[p], and using the index value of the peak spectrum line X[p] as the estimated value of the integer part frequency p;

[0096] The module for obtaining the estimated value of the fractional frequency is used to calculate the value of the interpolated spectrum line X[p±0.5] of the half index in the left and right directions of the peak spectrum line X[p], and to determine the spectrum line used for estimation based on the calculated spectrum line value; and to calculate the fractional frequency based on the spectrum line used for estimation determined by the judgment. estimated value of;

[0097] An estimation result acquisition module is used to combine the estimated value of the integer part frequency p and the fractional part frequency The estimated value of the digital angular frequency is obtained Complete the frequency estimation of the audio sinusoidal signal.

[0098] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0099] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0100] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0101] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A method for estimating the frequency of an audio sinusoidal signal based on DFT, characterized in that: The following steps are involved: Collect the single-tone audio sinusoidal signal to be processed and obtain the observation signal sequence of N sample points; the sampling result in a noise-free environment is represented as a signal waveform , A, f and Represent the amplitude, frequency and phase of the sinusoidal signal respectively, is the discrete signal index, Expressed as , is the digital frequency of the signal, f S represents the sampling frequency, Digital frequency The integer part frequency and fractional part frequency of 、 ; Perform N-point discrete Fourier transform on the observed signal sequence of the N sample points to obtain the transformed signal DFT spectrum line sequence X[k], which is expressed as: ， Where, is the DFT coefficient index; i is the imaginary number symbol; Search the signal DFT spectrum line sequence X[k] to locate the spectrum line with the largest amplitude as the peak spectrum line X[p], and use the index value of the peak spectrum line X[p] as the estimated value of the integer part frequency p; Calculate the value of the interpolated spectrum line X[p±0.5] of half the index in the left and right directions of the peak spectrum line X[p], and determine the spectrum line used for estimation based on the calculated spectrum line value; calculate the fractional frequency based on the spectrum line used for estimation determined by the judgment estimated value of; Combine the estimated value of the integer part frequency p and the fractional part frequency The estimated value of the digital angular frequency is obtained , complete the frequency estimation of the audio sinusoidal signal; The interpolated spectrum line X[p±0.5] values ​​of half the indexes in the left and right directions of the peak spectrum line X[p] are calculated, and the spectrum line used for estimation is determined based on the spectrum line values ​​obtained by calculation; the fractional frequency is calculated based on the spectrum line used for estimation determined by judgment. The steps for estimating the value include: When X[p-0.5]> X[p+0.5], if , then use X[p-1] and X[p] to obtain the estimated value of δ, the calculation expression is ;if , at this time, use X[p-0.5] and X[p+0.5] to obtain the estimated value of δ, and the calculation expression is ; In other cases, use X[p-0.5] and X[p] to obtain the estimated value of δ, and the calculation expression is ; is the fitting function; When X[p-0.5]< X[p+0.5], if , at this time, use X[p+1] and X[p] to obtain the estimated value of δ, and the calculation expression is ;if , at this time, use X[p-0.5] and X[p+0.5] to obtain the estimated value of δ, and the calculation expression is ; In other cases, X[p+0.5] and X[p] are used to obtain the estimated value of δ, and the calculation expression is .

2. A DFT-based audio sinusoidal signal frequency estimation system, characterized in that: include: The observation signal sequence acquisition module is used to collect the single-tone audio sinusoidal signal to be processed and obtain the observation signal sequence of N sample points; the sampling result in a noise-free environment is represented as a signal waveform , A, f and Represent the amplitude, frequency and phase of the sinusoidal signal respectively, is the discrete signal index, Expressed as , is the digital frequency of the signal, f S represents the sampling frequency, Digital frequency The integer part frequency and fractional part frequency of 、 ; The integer part frequency estimation value acquisition module is used to perform N-point discrete Fourier transform on the observed signal sequence of the N sample points to obtain the transformed signal DFT spectrum line sequence X[k], which is expressed as follows: ， Where, is the DFT coefficient index; i is the imaginary number symbol; search the signal DFT spectrum line sequence X[k] to locate the spectrum line with the largest amplitude as the peak spectrum line X[p], and use the index value of the peak spectrum line X[p] as the estimated value of the integer part frequency p; The module for obtaining the estimated value of the fractional frequency is used to calculate the value of the interpolated spectrum line X[p±0.5] of the half index in the left and right directions of the peak spectrum line X[p], and to determine the spectrum line used for estimation based on the calculated spectrum line value; and to calculate the fractional frequency based on the spectrum line used for estimation determined by the judgment. estimated value of; An estimation result acquisition module is used to combine the estimated value of the integer part frequency p and the fractional part frequency The estimated value of the digital angular frequency is obtained , complete the frequency estimation of the audio sinusoidal signal; The interpolated spectrum line X[p±0.5] values ​​of half the indexes in the left and right directions of the peak spectrum line X[p] are calculated, and the spectrum line used for estimation is determined based on the spectrum line values ​​obtained by calculation; the fractional frequency is calculated based on the spectrum line used for estimation determined by judgment. The steps for estimating the value include: When X[p-0.5]> X[p+0.5], if , at this time, use X[p-1] and X[p] to obtain the estimated value of δ, and the calculation expression is ;if , at this time, use X[p-0.5] and X[p+0.5] to obtain the estimated value of δ, and the calculation expression is ; In other cases, use X[p-0.5] and X[p] to obtain the estimated value of δ, and the calculation expression is ; is the fitting function; When X[p-0.5]< X[p+0.5], if , at this time, use X[p+1] and X[p] to obtain the estimated value of δ, and the calculation expression is ;if , at this time, use X[p-0.5] and X[p+0.5] to obtain the estimated value of δ, and the calculation expression is ; In other cases, X[p+0.5] and X[p] are used to obtain the estimated value of δ, and the calculation expression is .

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