Frequency resolution using compression

Abstract

In a frequency analysis system, such as a signal detection system or a spectrum analyzer, the frequency domain resolution is enhanced by compression and decompression of the signal samples. The limited capacity of the data storage and/or data transfer resources limit the number of samples that can be stored or transferred. A compressor forms a compressed signal prior to data transfer or storage. A decompressor decompresses the compressed signal prior to transformation to the frequency domain, by a fast Fourier transform or other frequency domain transform. The frequency domain resolution is enhanced because more decompressed samples are available for the frequency domain transform. The compressor and decompressor apply computationally efficient algorithms that can be implemented to operate in real time.

1 . In a frequency analysis system, a method for producing a frequency domain representation having a desired frequency domain resolution, wherein an input signal to the frequency analysis system is represented by signal samples having a sample rate and an uncompressed bit rate, wherein the frequency analysis system includes a data interface having an allocated capacity for storage or transfer of the signal samples that is limited to fewer than N of the signal samples at the uncompressed bit rate, the method comprising:
 determining a number N of signal samples based on the desired frequency domain resolution, wherein the sample rate divided by N approximately equals the desired frequency domain resolution;   compressing the N signal samples to form compressed signal samples having a compressed bit rate, wherein the compressed bit rate is less than or equal to the allocated capacity;   transferring the compressed signal samples through the data interface;   decompressing the compressed signal samples to form N decompressed signal samples; and   calculating a frequency domain transformation the N decompressed signal samples to form frequency domain samples of the frequency domain representation having a frequency domain resolution that is less than or equal to the desired frequency domain resolution.   
   
   
       2 . The method of  claim 1 , wherein the signal is an analog signal, the method further comprising:
 converting the analog signal to a digital form sampled at the sample rate and the uncompressed bit rate to produce the signal samples.   
   
   
       3 . The method of  claim 1 , wherein the data interface comprises a data storage device, the step of transferring further comprising storing the compressed signal samples in the data storage device and retrieving the compressed signal samples from the data storage device. 
   
   
       4 . The method of  claim 1 , wherein the data interface comprises a data transfer interface, the step of transferring further comprising transferring the compressed signal samples via the data transfer interface and receiving the compressed signal samples from the data transfer interface. 
   
   
       5 . The method of  claim 1 , wherein the frequency domain transformation is a discrete Fourier transform (DFT), a fast Fourier transform (FFT), a discrete sine transform (DST), a discrete cosine transform (DCT) or a z-transform. 
   
   
       6 . The method of  claim 1 , wherein the step of calculating a frequency domain transformation further comprises calculating magnitudes of the frequency domain samples to form a magnitude spectrum. 
   
   
       7 . The method of  claim 1 , wherein the step of compressing the N signal samples forms the compressed signal samples at a rate that is at least as fast as the sample rate.