Filtering of data sequence using OSM & OAM

In the fourth experiment we perform OAM and OSM. Fast convolution can be accomplished by overlap add(OA) or Overlap save(OS) methods.
Two methods are used to evaluate the discrete convolution −

Overlap-save method : If the components are observed, the
values from both convolutions result in the desired “fully engaged” filter during this region in
time. Therefore, overlapping smaller length convolutions and then summing the appropriate
overlapping segments will form the continuous output. This approach is called the “OverlapAdd
Method” for continuous signal processing.

Overlap-add method : Overlap–save is the traditional name for an efficient way to evaluate the discrete convolution
between a very long signal x(n) and a finite impulse response (FIR) filter h(n).

Fast Fourier Transform

In the third experiment we pwerform FFT. The Fast Fourier Transform (FFT) is one of the most important in signal processing and data analysis, but the FFT is a complicated algorithm.
In complex notation, the time and frequency domains each contain one signal made up of N complex points. Each of these complex points is composed of two numbers, the real part and the imaginary part.
The FFT operates by decomposing an N point time domain signal into N time domain signals each composed of a single point. The second step is to calculate the N frequency spectra corresponding to these N time domain signals. Lastly, the N spectra are synthesized into a single frequency spectrum.

Discrete Fourier Transform spectrum

In the second experiment we study the magnitude spectrum of DFT signal. The discrete Fourier transform takes in data and gives out the frequencies that the data contains.
This is useful if you want to analyze data, but can also be useful if you want to modify the frequencies then use the inverse discrete Fourier transform to generate the frequency modified data.
The shape of the time domain waveform is not important in these signals; the key information is in the frequency, phase and amplitude of the component sinusoidal.
The DFT is used to extract this information.

Linear convolution and circular convolution

In the first experiment we performed the Linear convolution and circular convolution.

Linear convolution: Linear convolution shifts linearly. It is operation to calculate the output for any linear time invariant system given its input and its impulse response. we can perform linear convolution from circular convolution, but the thing zero padding must be done upto L+M-1 inputs.

Circular convolution: Circular convolution shifts circularly. It is the same as linear convolution but considering that the support of the signal is periodic. Convolution is done but in circular pattern, depending upon the samples of the signal.