Abstract
Filters are very commonly found in everyday life and include examples such as water filters for water purification, mosquito nets that filter out bugs, bouncers at bars filtering the incoming guests according to age (and other criteria), and air filters found in air conditioners that we are sometimes a bit too lazy to change/clean periodically. Filters have two uses: signal separation and signal restoration. Signal separation is needed when a signal has been contaminated with interference, noise, or other signals. For example, imagine a device for measuring the electrical activity of a baby's heart (EKG) while still in the womb. The raw signal will likely be corrupted by the breathing and heartbeat of the mother. A filter might be used to separate these signals so that they can be individually analyzed. Signal restoration is used when a signal has been distorted in some way. For example, an audio recording made with poor equipment may be filtered to better represent the sound as it actually occurred [1, 2]. The main goal of this work is to study the exponential  window function and analyze a digital low pass FIR filter using the same in MATLAB. Properties of window functions is studied and frequeny domain responses of window functions is obtained. Then FIR filter is designed using widow design method and its characteristics have also been studied in frequency domain. The performace comparison between LPFs designed using other well known windows like Kaiser, Exponential, Cosh and modified kaiser window is done and it has been intuitively shown that for a given order and transition width, the filter designed using Exponential window provides the worse minimum stop band attenuation but better far end attenuation than filter designed by well known Kaiser Window.
Highlights
Digital filters are the most important and frequently used elements in digital signal processing applications
Where bi are the coefficients of transfer function numerator and are the coefficients of transfer function denominator modified kaiser window is done and it has been intuitively shown that for a given order and transition width, the filter designed using Exponential window provides the worse minimum stop band attenuation but better far end attenuation than filter designed by well known Kaiser Window
As we have analyzed the performace of an finite impulse response (FIR) filter using Exponential Window, so first of all the plots regarding window function are being shown
Summary
Digital filters are the most important and frequently used elements in digital signal processing applications. A computer program running on a CPU or a specialized DSP (or less often running on a hardware implementation of the algorithm) calculates an output number stream. This number stream is filtered by convolving it with the impulse response of the Filter. A digital filter is having several advantages: It is programmable, i.e. its operation is determined by a program stored in the processor's memory This means the digital filter can be changed without affecting the circuitry (hardware). Digital filters do not suffer from these problems, and so are extremely stable with respect both to time and temperature Unlike their analog counterparts, digital filters can handle low frequency signals accurately. As the speed of DSP technology (2) where; N is the order of the FIR filter and the length of the filter equal to N+1
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