Integrated circuit implementation of methods and apparatuses for monitoring occupancy of wideband GHz spectrum, and sensing respective frequency components of time-varying signals using sub-nyquist criterion signal sampling

An integrated circuit apparatus to determine an N-point Fast Fourier Transform (FFT) of a time-varying signal so as to sense one or more frequency components of the time-varying signal, the apparatus comprising:

• an input/output interface to receive a first sub-sampled set of samples of the time-varying signal sampled at a first sampling rate below a Nyquist rate of the time-varying signal and a second sub-sampled set of samples of the time-varying signal sampled at a second sampling rate below the Nyquist rate of the time-varying signal, wherein the second sampling rate is different from the first sampling rate;
• and
• at least one processor communicatively coupled to the input/output interface to:
• A) compute a first Fast Fourier Transform (FFT) for the first sub-sampled set of samples of the time-varying signal;
• and
• B) compute a second FFT for the second sub-sampled set of samples of the time-varying signal,
• wherein:
• each of the first FFT and the second FFT is a low-radix FFT;
• the input/output interface is configured to provide to the at least one processor:
• the first sub-sampled set of samples at the first sampling rate;
• the second sub-sampled set of samples at the second sampling rate;
• a third sub-sampled set of samples at the first sampling rate and time-shifted from the first sub-sampled set by a first number of samples;
• and
• a fourth sub-sampled set of samples at the second sampling rate and time-shifted from the second sub-sampled set by a second number of samples;
• and
• the at least one processor further is configured to compute:
• C) a third FFT for the third sub-sampled set of samples of the time-varying signal;
• and
• D) a fourth FFT for the fourth sub-sampled set of samples of the time-varying signal, wherein the N-point FFT of the time-varying signal is based at least in part on A), B), C) and D).

An Application Specific Integrated Circuit (ASIC) apparatus to determine an N-point Fast Fourier Transform (FFT) of a sampled time-varying signal so as to sense one or more frequency components of the sampled time-varying signal, the time-varying signal having a frequency bandwidth of interest BW and a Nyquist sampling criteria of N samples in a sampling time T, wherein N=T×BW, the sampled time-varying signal including a first sub-sampled set of B1 samples of the time-varying signal and a second sub-sampled set of B2 samples of the time-varying signal, the apparatus comprising:

• an input/output interface to receive the first sub-sampled set of B1 samples and the second sub-sampled set of B2 samples, wherein B1=N/p1, B2=N/p2, and wherein p2 and pi are co-prime numbers and both less than N;
• and
• at least one processor communicatively coupled to the input/output interface to:
• A) compute a first B1-point Fast Fourier Transform (FFT) for the first set of B1 samples of the time-varying signal;
• B) compute a second B2-point FFT for the second set of B2 samples of the time-varying signal;
• and
• C) compute the N-point FFT of the sampled time-varying signal based at least in part on A) and B),
• wherein:
• each of the first B1-point FFT and the second B1-point FFT is a low-radix FFT;
• and
• the input/output interface is configured to output the N-point FFT from C) so as to provide an indication of the one or more frequency components of the sampled time-varying signal.

An application specific integrated circuit (ASIC) apparatus for calculating a Fast Fourier Transform (FFT) of a signal, the ASIC apparatus comprising:

• an input/output interface adapted to receive a discrete z-point signal, z being a product of at least two numbers;
• one or more first xn-word memory blocks configured to store xn signal points sub-sampled by z/xn from the z-point signal;
• one or more second ym-word memory blocks configured to store ym signal points sub-sampled by z/ym from the z-point signal, wherein x and y are co-prime numbers and n and m are natural numbers, and
• a microprocessor for calculating the FFT of the signal, the microprocessor comprising:
• a bucketization microarchitecture to sub-sample the received signal and alias signal points to buckets whose number is less or equal to z, and
• a reconstruction microarchitecture designed to estimate a magnitude value and a frequency index of one or more frequency components of the z-point signal.