SignalUtils

If the parameters to CZT function do not change between calls, some variables can be pre-computed and stored in to a state variable. The length (and precision) of the source data is expected to remain fixed. This overload is about 2.5x faster than the variant without the state variable. 

The State variable does not need to be freed, if parameters change. It is also safe to call CztInit, if parameters did not change. Initialization will be simply skipped in this case. 

Chirp z transform transforms the time domain signal Src in to frequency domain (as do DFT and FFT). FStart is the starting frequency and FStop is the stop frequency. k defines the number of steps within that frequency band. FS is the sampling frequency. RStart is the starting radius of the circle in the z-domain and RStop is the final radius of the circle in the z-domain. CZT does the same as the FFT algorithm, if k = Src.Length*0.5, FStart = 0 and FStop = FS/2. and Src.Length is power of two. CZT is slower, but more versatile then FFT. It can be faster then FFT, for large zero padding factors. 

Chirp transform algorithm was first proposed by Bluestein. Generalization of the algorithm called Chirp-Z transform obtains samples of the z-transform spaced equally in angle on a spiral contour in z-plane. More on this subject can be found in [1] (p. 629) and [2] (p. 393). Rabiner [2] proposed the CZT algorithm. 

References:  

[1] Discrete-time signal processing, Oppenheim and Schafer, Prentice-Hall, 1989.  

[2] Theory and application of digital signal processing, Lawrence R. Rabiner and Bernard Gold. Prentice-Hall, 1975.

FrequencyResponse

Functions