OAM & OSM

 The fourth experiment of the course was on Linear FIR Filtering Methods -Overlap-add method and Overlap save method are algorithms to compute DFT of input signals of very large lengths. In OAM, the input signal is divided into small chunks of equal length and the convolution of these small chunks with the second signal is carried out. This can result into overlapping of values for the same indexes depending on the length of one chunk and the second input signal. Thus the output signal to be obtained should be addition of all the overlapped values.

In OSM, instead of dividing the input, we divide the output in small chunks and use only those input values which are required to calculate this output. Both the OAM and OSM require same amount of computations and hence memory.

Discrete Fourier Transform

The second experiment was of Discrete Fourier Transform . DFT (Discrete Fourier Transform) is carried out to overcome the limitation of Fourier series as well as DTFT. As length of signal increases, frequency spacing reduces, approximation error representation of spectrum decreases, resolution of spectrum increases, missing values in less point DFT are present in more point DFT.

FFT

 The third experiment was of Fast Fourier Transform.The FFT algorithm divides the N-point DFT input signal into 2 parts-even and odd signal values of the input. The even signal values can be directly found out whereas the odd signal values is just multiplied by an appropriate twiddle factor which overall reduces the complex multiplications for FFT.

Convolution and Correlation

                 In this experiment, we performed linear convolution, circular convolution, linear by circular convolution and auto and cross correlation. We used C code for programming all the cases.For N<L+M-1 the convoluted output signal has signal value overlap. This is known as aliasing effect. 

               Correlation is used to find out similarity between signals.The output signal due to auto-correlation was found to symmetric.