A comparative study on Main and Side lobe of frequency response curve for FIR Filter using Frequency Series Expansion Method

Abstract

The spectral contents of a frequency response curve can be modified by the system which is called as filter. To design a filter, the specifications must be used and the calculation of filter coefficients leads to approximate the desired frequency response. When a causal structure and non-recursive in nature with linear phase characteristics is used, the filter will be called as Finite Impulse Response (FIR).The FIR filter can be formed using Fourier Series Expansion Method. The Impulse Response of the filter is designed in discrete time (DT) domain with period equal to 2π considering the response between -π to +π in Fourier Series Expansion Method. So the length of the response is fixed and finite. The value π corresponds to the Nyquist Frequency (FN) which is equal to FS/2 where FS is the sampling frequency of the impulse response of the filter. In this paper the response curves for Low Pass, High Pass and Band Pass FIR Filter are observed and compared for different sampling frequency using Fourier Series Expansion Method. The main lobe and side lobe from the characteristics curves are also compared for different types of filters.