A method and circuit for ultra-wideband instantaneous frequency measurement

Abstract

The present application provides an ultra-wideband instantaneous frequency measurement method and circuit. The method includes: acquiring a radio frequency signal, folding the radio frequency signal at a certain moment based on a local oscillator signal to obtain a target sampling signal; performing a signal type conversion on the target sampling signal within a preset signal processing frequency band to obtain a digital signal; demodulating the digital signal first and then measuring the frequency according to the demodulated signal, so as to restore the instantaneous frequency before the radio frequency signal is folded, complete the analog processing of the digital signal, and no additional analog frequency conversion processing is required. The ultra-wideband instantaneous frequency measurement method provided by the present application breaks through the limitation of the Nyquist sampling theorem, folds the radio frequency signal first to obtain a relevant signal that meets the signal processing of the analog-to-digital converter, can directly use a single analog-to-digital converter to receive and process the ultra-wideband radio frequency signal, and restore the instantaneous frequency value of the relevant radio frequency signal, without other analog processing circuits.

Description

Technical Field

[0001] The present invention relates to the technical field of radio frequency circuits, and particularly to an ultra-wideband instantaneous frequency measurement method and circuit. Background Art

[0002] Receivers in the communication field are used to receive various radio signals and convert them into corresponding audio, video, or digital signals. With the continuous update of technology, all-digital receivers are the current development direction, which can directly perform analog-to-digital conversion on the signals sent by the antenna and do not require additional analog frequency conversion devices. However, limited by the sampling frequency of the analog-to-digital converter, analog-to-digital conversion cannot synchronously process signals in the entire frequency band. In related technologies, the signal receiving system is limited by the analog-to-digital converter, and the signal bandwidth needs to be less than the first Nyquist region of the analog-to-digital converter, that is, fs / 2. When the signal bandwidth is greater than the first Nyquist region: on the one hand, the entire measured bandwidth can be traversed step by step at fs / 2 each time by means of frequency sweeping, but this method cannot receive or cannot fully receive instantaneously generated signals, and the signal receiving speed is relatively slow; on the other hand, the entire frequency domain is segmented based on the fs / 2 frequency, and signals are obtained segment by segment. At least 2BW / fs channels are required to achieve full-band coverage, but this method not only has a complex design structure but also a high cost, which is not conducive to large-scale applications.

[0003] Therefore, how to provide a technical solution for real-time receiving and measuring the instantaneous frequency of ultra-wideband is a technical problem that needs to be solved urgently at present. Summary of the Invention

[0004] In view of the above-mentioned disadvantages of the prior art, the present invention provides a technical solution for ultra-wideband instantaneous frequency measurement to solve at least one of the above technical problems.

[0005] To achieve the above and other related objectives, the technical solutions provided in this application are as follows.

[0006] According to the first aspect of the embodiments of this application, an ultra-wideband instantaneous frequency measurement method is provided, including:

[0007] Obtain a radio frequency signal;

[0008] Perform signal folding on the radio frequency signal at a certain moment based on a local oscillator signal to obtain a target sampling signal, where the target sampling signal is within a preset signal processing frequency band, and the local oscillator signal corresponds to the signal modulation bandwidth of the baseband signal;

[0009] Perform signal conversion on the target sampling signal to obtain a digital signal;

[0010] Demodulate the digital signal, and perform frequency measurement based on the demodulated signal to obtain the instantaneous frequency, where the instantaneous frequency is consistent with the frequency of the RF signal before folding.

[0011] In an embodiment of the present application, perform signal folding on the RF signal at a certain moment based on the local oscillator signal to obtain a target sampling signal, including: performing multiple signal foldings on the RF signal based on the local oscillator signal to obtain multiple folded signals; performing filtering processing on the multiple folded signals according to a preset filter cut-off frequency to obtain the target sampling signal.

[0012] In an embodiment of the present application, perform multiple signal foldings on the RF signal based on the local oscillator signal to obtain multiple folded signals, including: folding the RF signal according to the center frequency of the local oscillator signal to determine the center frequency of each folded signal; determining the signal modulation bandwidth of the folded signal based on the signal modulation bandwidth of the local oscillator signal and the number of foldings.

[0013] In an embodiment of the present application, demodulate the digital signal, and perform frequency measurement based on the demodulated signal to obtain the instantaneous frequency, including: demodulating the digital signal to obtain the target sampling signal; determining the Nyquist region of the RF signal according to the signal modulation bandwidth of the target sampling signal and the signal modulation bandwidth of the local oscillator signal; measuring the instantaneous frequency according to the Nyquist region, the center frequency of the target sampling signal, and the center frequency of the local oscillator signal.

[0014] In an embodiment of the present application, the expression for determining the center frequency of the folded signal is as follows:

[0015] f2 = f1 - nf C

[0016] In the above expression, f2 is the center frequency of the folded signal, f1 is the RF signal, n is the number of foldings, and f c is the center frequency of the local oscillator signal.

[0017] According to the second aspect of the embodiments of the present application, there is provided an ultra-wideband instantaneous frequency measurement circuit, including:

[0018] A signal folding module, connected to the local oscillator signal and the RF signal, performing multiple signal foldings on the RF signal at a certain moment according to the local oscillator signal to obtain multiple folded signals, where there is a signal within a preset signal processing frequency band among the multiple folded signals, and the local oscillator signal corresponds to the signal modulation bandwidth of the baseband signal;

[0019] A signal processing module, connected to the signal folding module, converts the folded signal within the preset signal processing frequency band to obtain a digital signal;

[0020] A frequency determination module, connected to the signal processing module, demodulates the digital signal and measures the frequency based on the demodulated signal to obtain the instantaneous frequency of the RF signal before folding.

[0021] In an embodiment of the present application, the signal folding module includes: a signal generation unit for providing the baseband signal and migrating the frequency of the baseband signal to a preset frequency threshold to generate the local oscillator signal; a signal folding unit for folding the RF signal according to the center frequency of the local oscillator signal to obtain a plurality of the folded signals.

[0022] In an embodiment of the present application, the signal processing module includes: a filtering unit for filtering a plurality of the folded signals according to a preset filter cut-off frequency to obtain a target sampling signal; an analog-to-digital conversion unit for performing analog-to-digital signal conversion on the target sampling signal to obtain the digital signal.

[0023] In an embodiment of the present application, the frequency determination module includes: a signal demodulation unit for demodulating the digital signal to obtain the target sampling signal; a frequency measurement unit for determining the Nyquist region of the RF signal according to the signal modulation bandwidth of the target sampling signal and the signal modulation bandwidth of the local oscillator signal, and determining the instantaneous frequency according to the Nyquist region of the RF signal.

[0024] The present application provides an ultra-wideband instantaneous frequency measurement method and circuit. The method includes: acquiring an RF signal, folding the RF signal at a certain moment based on a local oscillator signal to obtain a target sampling signal; performing signal type conversion on the target sampling signal within a preset signal processing frequency band to obtain a digital signal; first demodulating the digital signal and then measuring the frequency according to the demodulated signal, so as to restore the instantaneous frequency of the RF signal before folding, complete the analog processing of the digital signal, and do not require additional analog frequency conversion processing. The ultra-wideband instantaneous frequency measurement method provided by the present application breaks through the limitation of the Nyquist sampling theorem, first folds the RF signal to obtain a relevant signal that meets the signal processing of the analog-to-digital converter, can directly use a single analog-to-digital converter to receive and process the ultra-wideband RF signal, and restore the instantaneous frequency value of the relevant RF signal, without other analog processing circuits.

[0025] It should be understood that the above general description and subsequent detailed description are only exemplary and explanatory, and cannot limit the present invention. Description of the Drawings

[0026] The accompanying drawings here are incorporated into the specification and form a part of this specification, showing embodiments in accordance with the present invention, and are used together with the specification to explain the principles of the present invention. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts. In the drawings:

[0027] Figure 1 is a flowchart of a UWB instantaneous frequency measurement method shown in an exemplary embodiment of the present invention;

[0028] Figure 2 is a block diagram of a UWB instantaneous frequency measurement circuit shown in an exemplary embodiment of the present invention;

[0029] Figure 3 is a specific structural diagram of a UWB instantaneous frequency measurement circuit shown in an exemplary embodiment of the present invention. Detailed implementation manners

[0030] The following will describe the embodiments of the present invention with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for explaining the present invention and not for limiting the protection scope of the present invention.

[0031] It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Therefore, only the components related to the present invention are shown in the diagrams, rather than being drawn according to the number, shape, and size of the components in actual implementation. The type, quantity, and proportion of each component in actual implementation can be arbitrarily changed, and the component layout type may also be more complex.

[0032] In the following description, a large number of details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it is obvious to those skilled in the art that the embodiments of the present invention can be implemented without these specific details. In other embodiments, well-known structures and devices are shown in the form of block diagrams rather than in detail to avoid making the embodiments of the present invention difficult to understand.

[0033] The Nyquist sampling theorem, also known as the Shannon sampling theorem, describes the relationship between the sampling frequency and the signal spectrum and is the basic basis for the discretization of continuous signals. Specifically, to recover the analog signal without distortion, the sampling frequency fs should be greater than or equal to 2 times the highest frequency fmax in the analog signal spectrum, i.e., fs ≥ 2fmax.

[0034] Receivers in the field of communication are used to receive various radio signals and convert them into corresponding audio, video, or digital signals. With the continuous update of technology, all-digital receivers are the current development direction. They can directly perform analog-to-digital conversion on the signals sent by the antenna and do not require additional analog frequency conversion devices. However, limited by the sampling frequency of the analog-to-digital converter, analog-to-digital conversion cannot synchronously process signals in the entire frequency band. The signal receiving system is restricted by the sampling input frequency range of the analog-to-digital converter, and the highest frequency of the signal to be sampled needs to be less than the first Nyquist region of the analog-to-digital converter, i.e., fs / 2.

[0035] Generally, when the signal bandwidth is greater than the first Nyquist region: on the one hand, the entire measured bandwidth can be traversed by sweeping frequency, with each step being fs / 2. However, this method cannot receive or cannot fully receive the signals generated instantaneously, and the signal receiving speed is relatively slow. On the other hand, based on the fs / 2 frequency, the entire frequency domain is segmented and the signals are obtained segment by segment. At least 2BW / fs channels are required to achieve full-band coverage. For example, if the frequency of the signal to be sampled is 20 GHz and the maximum sampling rate of the analog-to-digital converter is 4 GHz, the number of channels required is:

[0036]

[0037] It can be seen that implementing signal sampling by designing channels not only has a complex design structure but also a high cost, which is not conducive to large-scale applications.

[0038] To solve the above problems, this application provides an ultra-wideband instantaneous frequency measurement method, including:

[0039] S110. Obtain a radio frequency signal;

[0040] S120. Fold the radio frequency signal at a certain moment based on the local oscillator signal to obtain a target sampling signal, where the target sampling signal is within the preset signal processing frequency band, and the local oscillator signal corresponds to the signal modulation bandwidth of the baseband signal;

[0041] S130. Perform signal conversion on the target sampling signal to obtain a digital signal;

[0042] S140. Demodulate the digital signal and perform frequency measurement based on the demodulated signal to obtain the instantaneous frequency, where the instantaneous frequency is the same as the frequency of the radio frequency signal before folding.

[0043] Specifically, the steps for obtaining the local oscillator signal include: obtaining a baseband signal and shifting the frequency of the baseband signal to obtain the local oscillator signal. Specifically, a baseband signal can be generated by a digital-to-analog converter, and the frequency of the baseband signal is shifted to obtain the local oscillator signal. For example, if the baseband signal generated by the analog-to-digital converter is 500 MHz ± 5 MHz, the signal is subjected to microwave mixing processing to convert the center frequency of the baseband signal to 4 GHz, and the local oscillator signal is obtained, and the local oscillator signal is 4 GHz ± 5 MHz.

[0044] Specifically, folding the radio frequency signal at a certain moment based on the local oscillator signal to obtain the target sampling signal includes: folding the radio frequency signal multiple times based on the local oscillator signal to obtain multiple folded signals; filtering the multiple folded signals according to the preset filter cut-off frequency to obtain the target sampling signal. Specifically, the radio frequency signal is folded multiple times according to the local oscillator signal, and each signal folding obtains a folded signal, thus obtaining multiple folded signals. However, not every folded signal satisfies the preset signal processing frequency band of the analog-to-digital converter. Therefore, the multiple folded signals can be filtered through a filter to obtain the target sampling signal that satisfies the preset signal processing frequency band of the analog-to-digital converter.

[0045] Specifically, folding the radio frequency signal multiple times based on the local oscillator signal to obtain multiple folded signals includes: folding the radio frequency signal according to the center frequency of the local oscillator signal to determine the center frequency of each folded signal; determining the signal modulation bandwidth of the folded signal based on the signal modulation bandwidth and the number of foldings of the local oscillator signal. Specifically, if the radio frequency signal is 17 GHz, folding the radio frequency signal twice based on the center frequency of the local oscillator signal of 4 GHz, the center frequency of the first folded signal obtained is (17 - 2×4) = 9 GHz. According to the signal modulation bandwidth of the local oscillator signal of 5 MHz and the number of foldings (2 times), the signal modulation bandwidth of the first folded signal is calculated to be 10 MHz. Therefore, the first folded signal is (9G ± 10M) Hz. Similarly, folding the radio frequency signal three times, the second folded signal is (5G ± 15M) Hz; folding the radio frequency signal four times, the third folded signal is (1G ± 20M) Hz.

[0046] More specifically, the expression for determining the center frequency of the folded signal is as follows:

[0047] f2 = f1 - nf C (1)

[0048] In expression (1), f2 is the center frequency of the folded signal, f1 is the radio frequency signal, n is the number of foldings, and f c is the center frequency of the local oscillator signal.

[0049] It should be noted that signal conversion is performed on the target sampling signal to obtain a digital signal, including: inputting the target sampling signal into an analog-to-digital converter to perform signal sampling conversion from an analog signal to a digital signal, and obtaining a digital signal. For example, the signal within 2 GHz can be retained only through a low-pass filter, and the obtained target sampling signal is (1G ± 20M) Hz, and then analog-to-digital conversion is performed to obtain a digital signal.

[0050] Specifically, signal demodulation is performed on the digital signal, and instantaneous frequency is obtained based on the demodulated signal, including: performing signal demodulation on the digital signal to obtain the target sampling signal; determining the Nyquist region of the radio frequency signal according to the signal modulation bandwidth of the target sampling signal and the signal modulation bandwidth of the local oscillator signal; measuring the instantaneous frequency according to the Nyquist region, the center frequency of the target sampling signal, and the center frequency of the local oscillator signal. Specifically, first perform signal demodulation on the digital signal, that is, restore the digital signal to an analog signal to obtain the target sampling signal 1G ± 20M) Hz, and calculate the Nyquist region of the radio frequency signal according to the signal modulation bandwidth 20 MHz of the target sampling signal and the signal modulation bandwidth 5 MHz of the local oscillator signal, for example:

[0051] 20 MHz / 5 MHz = 4 (NZ) (2)

[0052] In expression (2), 20 MHz is the signal modulation bandwidth of the target sampling signal, 5 MHz is the signal modulation bandwidth of the local oscillator signal, and 4 (NZ) represents the 4th Nyquist region.

[0053] Calculate the instantaneous frequency of the radio frequency signal according to the Nyquist region, the center frequency of the target sampling signal, and the center frequency of the local oscillator signal.

[0054] 1 GHz + 4 (NZ) × 4 GHz = 17 GHz (3)

[0055] It can be seen from expression (3) that 1 GHz is the center frequency of the target sampling signal, 4 (NZ) represents the 4th Nyquist region, and 4 GHz is the center frequency of the local oscillator signal.

[0056] It should be noted that the ultra-wideband instantaneous frequency measurement method provided in this application is not only applicable to the instantaneous frequency measurement of a single radio frequency signal, but also applicable to the instantaneous frequency measurement of multiple ultra-wideband radio frequency signals. The processing method of multiple radio frequency signals is the same as that of a single radio frequency signal, except that after signal folding, the obtained target sampling signals are different, and multiple target sampling signals corresponding to multiple radio frequency signals all meet the sampling frequency of the analog-to-digital converter.

[0057] It can be seen from the above description that this method breaks through the limitation of the Nyquist sampling theorem and can use a relatively low-speed analog-to-digital converter to obtain signals with a larger bandwidth.

[0058] In a second aspect, as Figure 2 shown, the present application also provides an ultra-wideband instantaneous frequency measurement circuit, including:

[0059] A signal folding module, which receives a local oscillator signal and a radio frequency signal, and performs multiple signal foldings on the radio frequency signal at a certain moment according to the local oscillator signal to obtain multiple folded signals. Among them, there are signals within a preset signal processing frequency band in the multiple folded signals, and the local oscillator signal corresponds to the signal modulation bandwidth of the baseband signal;

[0060] A signal processing module, which is connected to the signal folding module, and performs signal conversion on the folded signals within the preset signal processing frequency band to obtain digital signals;

[0061] A frequency determination module, which is connected to the signal processing module, demodulates the digital signals, and performs frequency measurement based on the demodulated signals to obtain the instantaneous frequency of the radio frequency signal before folding.

[0062] Specifically, the signal folding module includes: a signal generation unit, which is used to provide a baseband signal and shift the frequency of the baseband signal to a preset frequency threshold to generate a local oscillator signal; a signal folding unit, which is used to fold the radio frequency signal according to the center frequency of the local oscillator signal to obtain multiple folded signals. Specifically, as Figure 3 shown, the signal generation unit provides a baseband signal through a digital-to-analog converter, and performs frequency mixing and shifting on the baseband signal through a mixer to obtain a local oscillator signal; the signal folding unit performs folding processing on the radio frequency signal according to the local oscillator signal to obtain multiple folded signals.

[0063] More specifically, the signal processing module includes: a filtering unit, which is used to filter the multiple folded signals according to a preset filter cut-off frequency to obtain a target sampling signal; an analog-to-digital conversion unit, which is used to perform analog-to-digital signal conversion on the target sampling signal to obtain digital signals. Specifically, as Figure 3 shown, the filtering unit filters the multiple folded signals through a low-pass filter to obtain a target sampling signal that meets the preset signal processing frequency band of the analog-to-digital converter, and inputs the target sampling signal into the analog-to-digital converter ADC for sampling from an analog signal to a digital signal to obtain digital signals.

[0064] More specifically, as Figure 3 shown, the frequency determination module includes: a signal demodulation unit for demodulating the digital signals to obtain a target sampling signal; a frequency measurement unit for determining the Nyquist region of the radio frequency signal according to the signal modulation bandwidth of the target sampling signal and the signal modulation bandwidth of the local oscillator signal, and finally calculating the instantaneous frequency of the radio frequency signal before folding according to the Nyquist region of the radio frequency signal.

[0065] The present application provides an ultra-wideband instantaneous frequency measurement method and circuit. The method includes: acquiring a radio frequency signal, folding the radio frequency signal multiple times based on a local oscillator signal to obtain multiple folded signals, such that there is a target sampling signal within a preset signal processing frequency band among the multiple folded signals; performing signal type conversion on the target sampling signal to obtain a digital signal; demodulating the digital signal first and then measuring the frequency according to the demodulated signal, thereby restoring the instantaneous frequency of the radio frequency signal and completing the analog processing of the digital signal without the need for additional analog frequency conversion processing. The ultra-wideband instantaneous frequency measurement method of the present application breaks through the limitation of the Nyquist sampling theorem. First, the radio frequency signal is folded, and then relevant signals that meet the signal processing requirements of the analog-to-digital converter are selected from the multiple folded signals. A single analog-to-digital converter can be directly used to receive and process the radio frequency signal with ultra-wide bandwidth, and the frequency value of the relevant input signal can be restored without the need for other analog processing circuits.

[0066] The above embodiments are only used to exemplarily illustrate the principles and effects of the present invention, rather than to limit the present invention. Any person familiar with this technology can modify or change the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or changes completed by those with ordinary knowledge in the technical field without departing from the spirit and technical ideas disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. An ultra-wideband instantaneous frequency measurement method, characterized in that: include: Acquire radio frequency signals; Performing signal folding on the radio frequency signal at a certain moment based on the local oscillator signal to obtain a target sampling signal, wherein the target sampling signal is within a preset signal processing frequency band, and the local oscillator signal corresponds to a signal modulation bandwidth of a baseband signal; Performing signal conversion on the target sampling signal to obtain a digital signal; The digital signal is demodulated, and frequency measurement is performed based on the demodulated signal to obtain an instantaneous frequency, wherein the instantaneous frequency is consistent with the frequency of the radio frequency signal before being folded.

2. The ultra-wideband instantaneous frequency measurement method according to claim 1, characterized in that: Performing signal folding on the radio frequency signal at a certain moment based on the local oscillator signal to obtain a target sampling signal includes: Performing multiple signal folding on the radio frequency signal based on the local oscillator signal to obtain multiple folded signals; The plurality of folded signals are filtered according to a preset filter cutoff frequency to obtain a target sampling signal.

3. The ultra-wideband instantaneous frequency measurement method according to claim 2, characterized in that: The radio frequency signal is folded multiple times based on the local oscillator signal to obtain multiple folded signals, including: Folding the radio frequency signal according to the center frequency of the local oscillator signal to determine the center frequency of each folded signal; The signal modulation bandwidth of the folding signal is determined based on the signal modulation bandwidth of the local oscillator signal and the number of folding times.

4. The ultra-wideband instantaneous frequency measurement method according to claim 3, characterized in that: The digital signal is demodulated, and frequency measurement is performed based on the demodulated signal to obtain an instantaneous frequency, including: Performing signal demodulation on the digital signal to obtain the target sampling signal; Determine the Nyquist zone of the radio frequency signal according to the signal modulation bandwidth of the target sampling signal and the signal modulation bandwidth of the local oscillator signal; The instantaneous frequency is measured according to the Nyquist zone, the center frequency of the target sampling signal and the center frequency of the local oscillator signal.

5. The ultra-wideband instantaneous frequency measurement method according to claim 3, characterized in that: The center frequency determination expression of the folded signal is as follows: <h2 style=";text-align:left;direction:ltr">f2=f1-nf<h2 style=";text-align:left;direction:ltr"> C In the above expression, f2 is the center frequency of the folded signal, f1 is the RF signal, n is the number of folding times, and f c is the center frequency of the local oscillator signal.

6. An ultra-wideband instantaneous frequency measurement circuit, characterized in that: include: A signal folding module is connected to a local oscillator signal and a radio frequency signal, and performs multiple signal folding on the radio frequency signal at a certain moment according to the local oscillator signal to obtain multiple folded signals, wherein there is a signal within a preset signal processing frequency band among the multiple folded signals, and the local oscillator signal corresponds to the signal modulation bandwidth of the baseband signal; A signal processing module, connected to the signal folding module, performs signal conversion on the folded signal in the preset signal processing frequency band to obtain a digital signal; The frequency determination module is connected to the signal processing module, performs signal demodulation on the digital signal, and performs frequency measurement based on the demodulated signal to obtain the instantaneous frequency of the radio frequency signal before being folded.

7. The ultra-wideband instantaneous frequency measurement circuit according to claim 6, characterized in that: The signal folding module comprises: A signal generating unit, configured to provide the baseband signal and migrate the frequency of the baseband signal to a preset frequency threshold to generate the local oscillator signal; A signal folding unit is used to fold the radio frequency signal according to the center frequency of the local oscillator signal to obtain a plurality of folded signals.

8. The ultra-wideband instantaneous frequency measurement circuit according to claim 6, characterized in that: The signal processing module comprises: A filtering unit, used for filtering the plurality of folded signals according to a preset filtering cutoff frequency to obtain a target sampling signal; The analog-to-digital conversion unit is used to perform analog-to-digital signal conversion on the target sampling signal to obtain the digital signal.

9. The ultra-wideband instantaneous frequency measurement circuit according to claim 8, characterized in that: The frequency determination module comprises: A signal demodulation unit, used for performing signal demodulation on the digital signal to obtain the target sampling signal; A frequency measurement unit is used to determine the Nyquist zone of the radio frequency signal according to the signal modulation bandwidth of the target sampling signal and the signal modulation bandwidth of the local oscillator signal, and determine the instantaneous frequency according to the Nyquist zone of the radio frequency signal.

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