Abstract
Filters are used in electronic circuits to remove the unwanted frequency components from desired signals. A digital filter basically provide high attenuation to the unwanted ones and offer very low or ideally zero attenuation to desired signal components when it’s impulse response is adjusted as per requirement. For ideal filters, the length of such an impulse response is infinite and also the filter will be non-causal and unrealizable. So, we need to truncate this infinite impulse response to make it finite. For this truncation, we use window functions. Using window functions, we obtain a finite impulse response or simply FIR filter. The shape of a window in time domain decides the characteristics of resultant filter in frequency domain. Several window functions are available in literature. For the present work we have choosen the three parameter Cosh window for truncation of infinite impulse response. It is also called as modified Cosh window because it has been obtained by inserting a third parameter in the basic 2-parameter Cosh window function. The main goal of this work is to study this modified Cosh window and design a digital low pass FIR filter using the same in MATLAB. First of all the properties of window function are described and frequeny domain responses of window function is obtained. Then FIR filter is analyzed using window design method and it’s characteristics have also been studied in frequency domain.
Highlights
Digital filters are the most important and frequently used elements in digital signal processing applications
As we have analyzed the performace of an finite impulse response (FIR) filter designed using modified Cosh window.So first of all, the plots related to window function are being shown and plots related to low pass filter (LPF) are discussed
As ripple improves for window function, Minimum stop band attenuation (MSA) of designed filter gets improved
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. The resulting number stream output can be converted into an analog signal by passing it through a digital-to-analog converter. A finite impulse response (FIR) filter is a type of a signal processing filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. The implementation of FIR filters with non-recursive techniques guarantees stability
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