A hand-held spectrum analyzer real-time spectrum signal processing system and processing method

Abstract

The application discloses a handheld spectrum analyzer real-time spectrum signal processing system and processing method, the system comprises a pre-processing unit, an ADC unit, an FPGA and an ARM which are connected in sequence, the FPGA comprises a digital down conversion unit, a multi-rate decimation filter unit, a real-time FFT operation unit and a real-time detection unit which are connected in sequence, and a grid mapping unit, a vector connection unit and a fluorescence statistical unit which are connected with the real-time FFT operation unit in sequence, the ARM comprises a real-time spectrum diagram and waterfall diagram unit which is connected with the real-time detection unit, and a fluorescence display unit which is connected with the fluorescence statistical unit. The application adopts parallel frame real-time detection and vector connection-based digital fluorescence statistical method to compress multiple spectrum data, reduces the requirement of a large number of spectrum data on screen refreshing, adopts vector connection to make fluorescence statistics, so that the measured signal is easier to distinguish, and the application meets the test requirement of a handheld instrument.

Description

Technical Field

[0001] This invention belongs to the field of spectrum analysis, and specifically relates to a real-time spectrum signal processing system and method for a handheld spectrum analyzer. Background Technology

[0002] With the increasing complexity of the electromagnetic spectrum environment and the large-scale application of 5G, any interference signal at any frequency point within the bandwidth of 5G NR base stations (around 100MHz) will affect the performance of base stations and even disrupt services. Therefore, the method of shutting down commercial base stations to investigate the source of interference becomes impractical.

[0003] Faced with complex broadband electromagnetic environments, ordinary sweep spectrum analyzers or receivers are no longer sufficient to acquire the characteristic parameters of interference signals. Real-time spectrum analysis can capture parameters such as the frequency, strength, duration, and bandwidth of interference signals. While some benchtop real-time spectrum analyzers can cover the occupied bandwidth of 5G NR, their large size and weight make them inconvenient to carry, especially in field testing where climbing is sometimes required, making them unsuitable for field interference troubleshooting. Some field testing instruments, although equipped with real-time spectrum functions, have insufficient bandwidth to fully cover the bandwidth of 5G base stations. Therefore, to pinpoint the location of interference sources, a portable real-time spectrum analyzer covering a 100MHz bandwidth suitable for field measurements is needed.

[0004] Currently available handheld real-time spectrum analyzers typically employ a method of seamlessly capturing and buffering IQ data before transmitting it to ARM software for processing. This software-based approach suffers from poor real-time performance due to the large data volume, long transmission time, and slow software processing speed. It is limited to real-time spectrum analysis of narrowband signals, and the large buffer capacity prevents real-time display; the buffer fills up after a period, causing data discontinuity and ceasing real-time operation. Furthermore, it increases size and power consumption.

[0005] While some handheld real-time spectrum analyzers can cover a 100MHz bandwidth, their digital fluorescence function, which distinguishes signals by color, lacks vector connection functionality. This results in discrete dot-like patterns on the measured stable signals, leading to a discrete dot-like spectrum. For single-tone signals with stable amplitude and frequency, the fluorescence pattern appears discontinuous and discrete. This method cannot display the true characteristics of the signal, making it difficult to distinguish signals. If there are multiple signals, it is even more difficult to distinguish them, and the true signal characteristics cannot be displayed intuitively.

[0006] To facilitate field testing, handheld measuring instruments have strict limitations on weight, size, and power consumption. Therefore, high-performance functions need to be developed based on low-cost, low-power FPGAs. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a real-time spectrum signal processing system and method for a handheld spectrum analyzer, aiming to reduce the screen refresh requirements for large amounts of spectrum data, make the measured signals easier to distinguish, and meet the testing needs of handheld instruments.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] A handheld spectrum analyzer real-time spectrum signal processing system includes a preprocessing unit, an ADC unit, an FPGA, and an ARM connected in sequence. The FPGA includes a digital down-conversion unit, a multi-rate decimation filtering unit, a real-time FFT operation unit, and a real-time detection unit connected in sequence, as well as a grid mapping unit, a vector connection unit, and a fluorescence statistics unit connected in sequence to the real-time FFT operation unit. The ARM includes a real-time spectrum plot and waterfall plot unit connected to the real-time detection unit, and a fluorescence display unit connected to the fluorescence statistics unit.

[0010] In the above scheme, the preprocessing unit includes an attenuator, a first bandpass filter, a first mixer, a second bandpass filter, a second mixer, and an intermediate frequency conditioner connected in sequence. The first mixer is connected to the first local oscillator, and the second mixer is connected to the second local oscillator.

[0011] A real-time spectrum signal processing method for a handheld spectrum analyzer includes the following steps:

[0012] Step (1): After passing through the preprocessing unit, the radio signal is converted into an analog intermediate frequency signal with a fixed center frequency and a bandwidth of 120MHz. The ADC unit samples the received analog intermediate frequency signal, converts the analog intermediate frequency signal into a digital intermediate frequency signal, and sends it to the digital downconversion unit.

[0013] Step (2): The digital downconversion unit performs digital downconversion on the digital intermediate frequency signal, and the multi-rate decimation filter unit performs multi-rate decimation and filtering to output baseband IQ data with variable real-time bandwidth.

[0014] Step (3): The real-time FFT operation unit performs real-time FFT operation on the baseband IQ data with variable real-time bandwidth to obtain multiple frames of FFT data;

[0015] Step (4): The real-time detection unit performs real-time detection on multiple frames of FFT data to obtain a single frame of spectrum. The real-time spectrum and waterfall plot units display the real-time spectrum and real-time waterfall plot based on this single frame of spectrum.

[0016] Step (5): The grid mapping unit performs grid mapping on the multi-frame FFT data, the vector connection unit performs vector connection on the grid-mapped data, the fluorescence statistics unit performs digital fluorescence statistics on the vector connection data, and finally the fluorescence display unit uses color to represent the number of times each grid is hit, thus realizing digital fluorescence display.

[0017] In the above scheme, in step (1), the ADC unit acquires a broadband signal with a center frequency of 276.48MHz and a bandwidth of 120MHz; the selected sampling rate must meet the requirements of real-time spectrum analysis of 120MHz bandwidth and demodulation analysis of 5G NR baseband signal;

[0018] Among them, the real-time spectrum analysis of the 120MHz broadband needs to meet the following requirements:

[0019] f s ≥2B

[0020]

[0021] Among them, the demodulation analysis of 5G NR baseband signals must meet the following requirements:

[0022] f s =122.88MHz*n, n=2,3,4……

[0023] In the formula, f s Where f is the sampling rate, B is the maximum real-time bandwidth, and f0 is the center frequency.

[0024] In the above scheme, in step (3), the real-time FFT operation unit adopts a resource-saving fully parallel FFT operation, which simplifies the number of FFT points by half. The spectra of the first and second halves are as follows:

[0025]

[0026]

[0027] Where X(k) is the spectrum of the first half, X(k+N / 2) is the spectrum of the second half, Y[k] and Z[k] are the FFT operations of N / 2 points of odd and even baseband IQ data, respectively, and N is the number of points of the Fast Fourier Transform. j is the imaginary unit.

[0028] In the above scheme, during step (4), the real-time detection process involves converting the original spectrum of the M frames [X]... 11 X 12 , ..., X 1(N-1) X 1N ], [X 21 X 22 , ..., X 2(N-1) X 2N],…,[X M1 X M2 , ..., X MN-1 X MN [X1, X2, ..., X] is compressed into a new frame of spectrum [X1, X2, ..., X]. (N-1) X N ], X MN X represents the amplitude value of the Nth frequency point of the FFT in the Mth frame. N It represents the amplitude value of the Nth frequency point of the compressed new frame FFT; and performs maximum, minimum, sampling or accumulation operations on the previous frame data and the current frame data.

[0029] In the above scheme, in step (5), the grid mapping method is as follows: First, the milliwatt value representing the power amplitude is converted into an absolute decibel value (dBm) through logarithmic operation, and the power is pre-adjusted and converted into a 582*512 matrix grid, where the rows represent the amplitude value and the columns represent the frequency value; the corresponding grid is filled according to the amplitude value corresponding to the current frequency, with 1 filled if it is hit and 0 filled if it is not hit.

[0030] Furthermore, the logarithmic operation is implemented using the CORDIC algorithm:

[0031]

[0032] log 10 AMP = lnAMP * log 10 e

[0033] Here, AMP represents the power amplitude value at the current frequency point.

[0034] In the above scheme, in step (5), the rule for the vector connection is: set the absolute decibel values ​​of the power corresponding to three adjacent frequency points as follows: A m-1 A m and A m+1 Where m is 1, 2, ..., N-2; N is the number of points in the Fast Fourier Transform;

[0035] (1) When filling the first column:

[0036] When A0≤A1, the first column is filled with 1 in the position corresponding to the data value of the first number, and 0 in the other positions.

[0037] When A0 > A1, the first column will fill the positions within the range of A1 to A0 with 1, and fill the other positions with 0;

[0038] (2) When the middle column is used:

[0039] When A m ≤min(A m+1 A m-1In this case, the current column will be filled with 1s in the positions corresponding to the current data value, and 0s in the other positions.

[0040] When A m >min(A m+1 A m-1 The current column will min(A) m+1 A m-1 ) to A m Fill the positions within the specified range with 1, and fill the other positions with 0;

[0041] (3) When it is the last column:

[0042] When A N-1 ≤A N-2 In the last column, simply fill the position corresponding to the data value of the current number with 1, and fill the other positions with 0;

[0043] When A N-1 >A N-2 The last column will be A M-2 To A M-1 Fill the positions within the specified range with 1s, and fill the other positions with 0s.

[0044] In the above scheme, during the fluorescence statistics in step (5), the matrix grid is split into 8 columns of 64×16bit BRAM for parallel processing. The area is used instead of the speed to complete all the occurrences in the statistics process. An interrupt is sent to the upper-layer software, and the image is drawn according to the number of hits.

[0045] Through the above technical solution, the real-time spectrum signal processing system and method for a handheld spectrum analyzer provided by the present invention have the following beneficial effects:

[0046] This invention is based on a handheld instrument platform and uses a low-cost, low-power FPGA to achieve real-time spectrum analysis at 120MHz. It employs parallel frame real-time detection and vector-connected digital fluorescence statistics to compress multiple calculated spectrum data points, reducing the screen refresh requirements for large amounts of spectrum data. The use of vector connections for fluorescence statistics makes the measured signals easier to distinguish, meeting the testing needs of handheld instruments. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0048] Figure 1 This is a schematic diagram of a real-time spectrum signal processing system for a handheld spectrum analyzer disclosed in an embodiment of the present invention.

[0049] Figure 2This is a schematic diagram of the connection between the ADC unit, FPGA and ARM disclosed in the embodiments of the present invention. Detailed Implementation

[0050] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0051] This invention provides a real-time spectrum signal processing system for a handheld spectrum analyzer, such as... Figure 1 As shown, it includes a preprocessing unit, an ADC unit, an FPGA, and an ARM connected in sequence, as follows: Figure 2 As shown, the FPGA includes a digital downconversion unit, a multi-rate decimation filter unit, a real-time FFT operation unit, and a real-time detection unit connected in sequence, as well as a grid mapping unit, a vector connection unit, and a fluorescence statistics unit connected in sequence to the real-time FFT operation unit. The ARM includes a real-time spectrum plot and waterfall plot unit connected to the real-time detection unit, as well as a fluorescence display unit connected to the fluorescence statistics unit.

[0052] Specifically, the preprocessing unit includes an attenuator, a first bandpass filter, a first mixer, a second bandpass filter, a second mixer, and an intermediate frequency conditioner connected in sequence. The first mixer is connected to the first local oscillator, and the second mixer is connected to the second local oscillator.

[0053] A real-time spectrum signal processing method for a handheld spectrum analyzer includes the following steps:

[0054] Step (1): The radio signal enters the preprocessing unit and is converted into an analog intermediate frequency signal with a fixed center frequency and a bandwidth of 120MHz after attenuation, two-stage mixing and intermediate frequency conditioning. The ADC unit samples the received analog intermediate frequency signal according to a certain sampling rate, converts the analog intermediate frequency signal into a digital intermediate frequency signal, and sends it to the digital downconversion unit in the FPGA through the JESD204B high-speed interface.

[0055] The ADC unit acquires a broadband signal with a center frequency of 276.48MHz and a bandwidth of 120MHz; the selected sampling rate must meet the requirements for real-time spectrum analysis of the 120MHz bandwidth and demodulation analysis of the 5G NR baseband signal.

[0056] Among them, the real-time spectrum analysis of the 120MHz broadband needs to meet the following requirements:

[0057] f s ≥2B

[0058]

[0059] Among them, the demodulation analysis of 5G NR baseband signals must meet the following requirements:

[0060] f s=122.88MHz*n, n=2,3,4……

[0061] In the formula, f s Where f is the sampling rate, B is the maximum real-time bandwidth, and f0 is the center frequency.

[0062] In this embodiment, the sampling rate of the ADC unit is 368.64MHz.

[0063] Step (2): The digital downconversion unit performs digital downconversion on the digital intermediate frequency signal, and the multi-rate decimation filter unit performs multi-rate decimation and filtering to output baseband IQ data with variable real-time bandwidth.

[0064] Step (3): The real-time FFT operation unit performs real-time FFT operations on the baseband IQ data with variable real-time bandwidth to obtain multiple frames of FFT data. Real-time operation requires that the speed of FFT operation for processing one frame of data is faster than the speed of acquiring one frame of data. If the clock rate of the FFT operation implemented inside the FPGA is equal to the IQ rate, the FFT calculation cannot complete the processing of one frame of data within the effective time, which will cause blocking. Therefore, it is necessary to increase the clock rate of FFT calculation. However, it is difficult to meet the timing convergence requirement of increasing the FFT calculation speed on low-cost FPGAs. Using pure parallel FFT calculation consumes a lot of resources, and low-power FPGA resources are limited and will increase power consumption. This invention adopts a resource-saving fully parallel FFT operation, which simplifies the number of FFT points by half to meet the requirements of real-time processing. The spectra of the first and second halves are as follows:

[0065]

[0066]

[0067] Where X(k) is the spectrum of the first half, X(k+N / 2) is the spectrum of the second half, Y[k] and Z[k] are the FFT operations of N / 2 points of odd and even baseband IQ data, respectively, and N is the number of points of the Fast Fourier Transform. j is the imaginary unit.

[0068] Step (4): The real-time detection unit performs real-time detection on multiple frames of FFT data to obtain a single frame of spectrum. The real-time spectrum and waterfall plot units display the real-time spectrum and real-time waterfall plot based on this single frame of spectrum.

[0069] High-speed data is processed in real time, generating a large amount of data per second that cannot be displayed or updated in real time. During real-time detection, the original spectrum of the M frames [X] is used. 11 X 12 , ..., X 1(N-1) X 1N ], [X 21 X 22 , ..., X2(N-1) X 2N ],…,[X M1 X M2 , ..., X MN-1 X MN [X1, X2, ..., X] is compressed into a new frame of spectrum [X1, X2, ..., X]. (N-1) X N ], X MN X represents the amplitude value of the Nth frequency point of the FFT in the Mth frame. N This represents the amplitude value of the Nth frequency point in the compressed new frame FFT; and performs maximum, minimum, sampling, or accumulation operations on the previous frame data and the current frame data. The compressed spectrum data is sent to the ARM via PCIe, where the ARM's real-time spectrum plot and waterfall plot units generate real-time spectrum plots, waterfall plots, and digital phosphors.

[0070] Step (5): The grid mapping unit performs grid mapping on the multi-frame FFT data, the vector connection unit performs vector connection on the grid-mapped data, the fluorescence statistics unit performs digital fluorescence statistics on the vector connection data, and finally the fluorescence display unit at the ARM end uses color to represent the number of times each grid is hit, thus realizing digital fluorescence display.

[0071] Specifically, the grid mapping method is as follows: First, the milliwatt value representing the power amplitude is converted into an absolute decibel value in dBm through logarithmic operation, and the power is pre-adjusted to convert it into a 582*512 matrix grid, where rows represent amplitude values ​​and columns represent frequency values; the corresponding grid is filled according to the amplitude value corresponding to the current frequency, with 1 filled if it is a match and 0 filled if it is not a match.

[0072] Logarithmic operations are converted into a CORDIC algorithm that can be implemented on an FPGA. Logarithmic operations can be converted using the arctangent, and the FPGA can implement the arctangent operation using CORDIC. Specifically, the logarithmic operation method is as follows:

[0073]

[0074] log 10 AMP = lnAMP * log 10 e

[0075] Here, AMP represents the power amplitude value at the current frequency point.

[0076] The rule for vector connections is as follows: Set the absolute decibel values ​​of the power corresponding to three adjacent frequency points as follows: A m-1 A m and A m+1 Where m is 1, 2, ..., N-2; N is the number of points in the Fast Fourier Transform;

[0077] (1) When filling the first column:

[0078] When A0≤A1, the first column is filled with 1 in the position corresponding to the data value of the first number, and 0 in the other positions.

[0079] When A0 > A1, the first column will fill the positions within the range of A1 to A0 with 1, and fill the other positions with 0;

[0080] (2) When the middle column is used:

[0081] When A m ≤min(A m+1 A m-1 In this case, the current column will be filled with 1s in the positions corresponding to the current data value, and 0s in the other positions.

[0082] When A m >min(A m+1 A m-1 The current column will min(A) m+1 A m-1 ) to A m Fill the positions within the specified range with 1, and fill the other positions with 0;

[0083] (3) When it is the last column:

[0084] When A N-1 ≤A N-2 In the last column, simply fill the position corresponding to the data value of the current number with 1, and fill the other positions with 0;

[0085] When A N-1 >A N-2 The last column will be A M-2 To A M-1 Fill the positions within the specified range with 1s, and fill the other positions with 0s.

[0086] During fluorescence statistics, the matrix grid is split into 8 columns of 64×16bit BRAM for parallel processing. The area is used instead of the speed to complete all the occurrences in the statistical process. An interrupt is sent to the upper-level software, and the image is drawn based on the number of hits.

[0087] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method of real-time spectral signal processing for a hand-held spectrum analyzer, comprising: Comprise the following steps: Step (1): the radio signal after pre-processing unit into a fixed center frequency, bandwidth of 120MHz analog intermediate frequency signal, ADC unit will receive the analog intermediate frequency signal sampling, analog intermediate frequency signal into digital intermediate frequency signal, and send to digital down conversion unit; Step (2): digital down conversion unit for digital intermediate frequency signal digital down conversion, multi-rate extraction filter unit for multi-rate extraction, filter output variable real-time bandwidth baseband IQ data; Step (3): real-time FFT operation unit for variable real-time bandwidth baseband IQ data do real-time FFT operation, get multiple frame FFT data; Step (4): real-time detection unit for multiple frame FFT data real-time detection get a frame spectrum, real-time spectrum and waterfall chart unit based on this a frame spectrum display real-time spectrum and real-time waterfall chart; Step (5): grid mapping unit for multiple frame FFT data grid mapping, vector connection unit for grid mapping after the data vector connection, fluorescence statistics unit for vector connection of the data for digital fluorescence statistics, finally by fluorescence display unit with color to represent each grid hit times, realize digital fluorescence display; In step (5), the rule of the vector connection is that the absolute decibel values of the powers corresponding to the adjacent three frequency points are respectively A m-1 , A m , and A m+1 , wherein m is 1, 2, …, N-2; N is the number of points of the fast Fourier transform. (1) when the first column filling: When A0≤A1, the first column directly fills the first number of data value corresponding to the position of 1, and other positions are filled with 0; When A0>A1, the first column fills the position from A1 to A0 with 1, and other positions are filled with 0; (2) when the middle column: When A m ≤ min(A m+1 , A m-1 ), the current column directly fills the position corresponding to the data value of the number with 1, and fills other positions with 0; When A m > min(A m+1 , A m-1 ), the current column fills in 1 for the positions in the range of min(A m+1 , A m-1 ) to A m , and 0 for the other positions; (3) when the last column: When A N-1 ≤ A N-2 , the last column directly fills the position corresponding to the data value of the number with 1, and other positions with 0; When A N-1 > A N-2 , the last column will be filled with 1 at positions in the range of A M-2 to A M-1 and 0 elsewhere.

2. A real-time spectral signal processing method for a hand-held spectrum analyzer according to claim 1, characterized in that, In step (1), the ADC unit collects a wideband signal with a center frequency of 276.48MHz and a bandwidth of 120MHz; the selected sampling rate needs to meet the real-time spectrum analysis of 120MHz bandwidth and the demodulation analysis of 5G NR baseband signal; Wherein, the real-time spectrum analysis of 120MHz wideband needs to meet: f s ≥2B Wherein, the demodulation analysis of 5G NR baseband signal needs to meet: f s = 122.88 MHz * n, n = 2, 3, 4... where f s is the sampling rate, B is the maximum real-time bandwidth, and f0is the center frequency.

3. The method of claim 1, wherein the method further comprises: In step (3), the real-time FFT operation unit adopts a resource-saving full parallel FFT operation, the FFT point number is simplified by half, and the spectra of the front and back halves are respectively: wherein X(k) is the spectrum of the first half, X(k+N / 2) is the spectrum of the second half, Y[k], Z[k] are FFT operations of N / 2 points of odd and even baseband IQ data respectively, and N is the number of points of fast Fourier transform, j is the imaginary unit.

4. The method of claim 1, wherein the method is a real-time spectrum signal processing method for a hand-held spectrum analyzer. In step (4), during real-time detection, the original spectrum of the M frames [X] is... 11 X 12 , ..., X 1(N-1) X 1N ], [X 21 X 22 , ..., X 2(N-1) X 2N ],…,[X M1 X M2 , ..., X MN-1 X MN [X1, X2, ..., X] is compressed into a new frame of spectrum [X1, X2, ..., X]. (N-1) X N ], X MN X represents the amplitude value of the Nth frequency point of the FFT in the Mth frame. N It represents the amplitude value of the Nth frequency point of the compressed new frame FFT; and performs maximum, minimum, sampling or accumulation operations on the previous frame data and the current frame data.

5. The method of claim 1 wherein, In step (5), the grid mapping method is as follows: first, convert the milliwatt value representing the power amplitude into absolute decibel value dBm through logarithmic operation, and perform power pre-adjustment, convert into 582*512 matrix grid, row represents amplitude value, list represents frequency value; fill in the corresponding grid according to the amplitude value corresponding to the current frequency, fill in 1, and fill in 0 without being hit.

6. A real-time spectral signal processing method for a hand-held spectrum analyzer according to claim 5, wherein, The logarithmic operation is realized by CORDIC algorithm: log 10 AMP = lnAMP * log 10 e Wherein, AMP represents the power amplitude value of the current frequency point.

7. The method of claim 1, wherein the method is a real-time spectrum signal processing method for a hand-held spectrum analyzer. In step (5), when the fluorescence statistics, the matrix grid is split into 8 columns of 64*16bit BRAM parallel processing, the area is replaced by the speed, all the times appearing in the statistical process are completed, the interrupt is sent to the upper layer software, and the image is drawn according to the hit times.

8. A hand-held spectrum analyzer real-time spectral signal processing system employing a hand-held spectrum analyzer real-time spectral signal processing method as claimed in claim 1, characterized by, It comprises a pre-processing unit, an ADC unit, an FPGA and an ARM connected in sequence, the FPGA comprises a digital down-conversion unit, a multi-rate decimation filter unit, a real-time FFT operation unit and a real-time detection unit connected in sequence, and a grid mapping unit, a vector connection unit and a fluorescence statistics unit connected in sequence with the real-time FFT operation unit, the ARM comprises a real-time spectrum and waterfall chart unit connected with the real-time detection unit, and a fluorescence display unit connected with the fluorescence statistics unit.

9. A hand-held spectrum analyzer real-time spectral signal processing system according to claim 8, wherein, The pre-processing unit comprises an attenuator, a band-pass filter one, a mixer one, a band-pass filter two, a mixer two and an intermediate frequency conditioner connected in sequence, the mixer one is connected with a first local oscillator, and the mixer two is connected with a second local oscillator.

Images