Discrete Fourier Transform

Second lab was based on DFT and IDFT. We have considered 2 cases. First case included calculation of 4 point DFT of input signal. Second case was appending the sequence x[n] by 4 zeros. DFT gives periodic result with period equal to N (length of input signal). We also performed IDFT (inverse discrete fourier transform) to find x[n] from X[k].

Fast Fourier Transform

In this lab session we performed FFT and IFFT. We performed 4-point and 8-point FFT. FFT algorithms are based on the fundamental principle of decomposing computation of the discrete fourier transform of a sequnce of length N into successively smaller discrete fourier transforms. As compared to DFT, FFT is much faster.

OAM and OSM

Overlap add method and overlap save method are block processing technique. Input data gets divided into smaller chunks on which convolution is performed to find output. The overlapped portion is discarded in OSM whereas it is added in OAM to get requird output. In the C code convolution of blocks is performed by using FFT.

Convolution and Correlation

The first  experiment was based on convolution and correlation. The developed code was compiled using a GCC compiler. Convolution is usually between a signal and filter ie. system with single input and stored coefficients. Correlation is usually between two signal ie. two inputs and no stored coefficients. Correlation is used to find out similarity between signals.
For convolution y[n]=x[n] * h[n]
For correlation y[n]=x[n] o h[n]