FILTERING OF LONG DATA SEQUENCE

        The aim of this experiment was to perform filtering of long data sequence using Overlap Add Method(OAM) and Overlap Save Method(OSM). These methods are used to find discrete convolution i.e. output of FIR filter for a very long input signal x(n).

        OAM and OSM divides the input sequence into smaller blocks. The filtering of individual blocks, which are smaller in length, is done by DFT and IDFT and then fitted one after the other. The overlapped portion is discarded in OSM whereas it is added in OAM to get the required output sequence. Thus, OAM and OSM are block processing techniques.

        They are suitable for real time signal processing. They are used for decreasing the delay obtained in getting the output.

FAST FOURIER TRANSFORM

        The aim of this experiment was to perform Fast Fourier Transform(FFT) of N point signal. We found out the FFT of 4 point and 8 point input sequence using DITFFT. We also performed Inverse Fast Fourier Transform(IFFT) to verify our original input signal.
        We observed that, input sequence order and output sequence order in Radix-2 FFT algorithm is in bit reversal manner. We compared the real and complex additions as well as the real and complex multiplications of FFT with DFT and came to a conclusion that FFT improves operational efficiency by parallel processing. Thus, FFT is computationally fast algorithm.

DISCRETE FOURIER TRANSFORM

        The aim of this experiment was to perform Discrete Fourier Transform(DFT) of N point signal. We found out the DFT of input signal x(n), zero padded x(n) and expanded signal. We also plotted the magnitude spectrum of these signals. We also performed Inverse Discrete Fourier Transform(IDFT) to verify our original input signal.
        We observed that, as the length of the signal increases by zero padding, frequency spacing decreases, approximation error decreases and resolution of spectrum increases. DFT gives approximated spectrum. Expansion of signal in time domain gives compressed spectra in frequency domain. Also, DFT is computationally slow. We found out the total number of real additions and multiplications using the code and verified it with the formulae available for these parameters.

DISCRETE CONVOLUTION AND CORRELATION

        The aim of this experiment was to study mathematical operations such as Linear Convolution, Circular Convolution, Linear Convolution using Circular Convolution and Correlation. In our practical session, we implemented these operations using C codes to find the output of the system and degree of similarity between the two signals.

        First part of this experiment was to find convolution between two signals x(n) and h(n). We found out that circular convolution gives aliased output.

        Second part of this experiment was to find correlation between two signals. We found the auto-correlation of input signal x(n) and also of delayed input signal. Auto-correlation output signal is an even signal. The auto-correlation of delayed input signal is same as that of auto-correlation of original signal. The application of correlation is to find the degree of similarity of two signals.