Overlap add method and overlap save method

Overlap Add and Overlap Save Methods are used to process real time signals. Both methods breakdown the signal into segments, process each segment and then combine the segments into one final output signal.of their speed. OAM and OSM are preferred for real time processing.
In the experiment OAM and OSM were applied on a 13 point sequence. 

Experiment three: Fast Fourier Transform

FFT rapidly computes transformations by factorising the DFT matrix into a product of a sparse factors. As a result the complexity of the computation is reduced.

In this experiment, we applied  the FFT algorithm to a 4 point and an 8 point sequence. We calculated the number of real multiplications and real additions.

Experiment two: Discrete Fourier Transform

Discrete Fourier Transform (DFT) is used to convert digital signal in time domain into a signal in the frequency domain.

It is used to calculate a signal's frequency spectrum.
In this experiment,we calculated DFT of 4 and 8 point sequences.The 8-point sequence was a zero padded 4-point sequence.

Learnings from experiment:

1.  Inverse DFT converges.
2.  DFT produces periodic results with period N.
3.  DFT coefficients are defined in the frequency range [0,2π].
4.  As N increases, frequency spacing reduces, approximation error decreases, resolution of spectrum increases.
5. As signal is expanded in time domain, spectrum is compressed in frequency domain.

Experiment one : Discrete Convolution and Correlation

Part one: Convolution

Convolution is used to find output of the system.

We calculated 

1. Linear convolution
2. Circular convolution
3. Linear convolution using circular convolution.

Learnings from experiment:

• In linear convolution, length of output signal is one less than the addition of length of both input signals.
• In circular convolution:

1) Length of output signal is same as that of input signal with higher length.
2) Last few values are aliased on initial few values. Hence we get aliased output.


Part two: Correlation
Correlation is used to find the degree of similarity between two signals.

We calculated 

1. Autocorrelation
2. Cross-correlation

Learnings from experiment:

• Autocorrelation is an even signal.
• Autocorrelation of delayed input signal is same as that of autocorrelation of original input signal.
• Cross-correlation of input signal with delayed input signal is same as advanced autocorrelated input signal.
• In cross-correlation of scaled input signal, output is scaled by same factor as that of input signal.