NAME: S.VAISHNAVI
ROLL NO.: 16011A0449 BRANCH: ECE-REGULAR
FIR LPF,HPF,BPF,BSF USING RECTANGULAR WINDOW
AIM: To design FIR lowpass, highpass, bandpass and bandstop filters using rectangular
window.
APPARATUS: Matlab R2018a
THEORY:
FIR filters. These filters are called finite impulse response filters. They are characterised by
the impulse response given as:
where the impulse response H(z) is of finite length ‘N’ and x(n) is the input sequence. The
windowing method requires minimum amount of computational effort; so window method is
simple to implement. For the given window, the maximum amplitude of ripple in the filter
response is fixed. Thus the stop band attenuation is fixed in the given window, but there is
some drawback also of this method. The design of FIR filter is not flexible. The frequency
response of FIR filter shows the convolution of spectrum of window function & desired
frequency response because of this; the pass band & stop band edge frequency cannot be
precisely specified. The rectangular window (sometimes known as the boxcar or Dirichlet
window) is the simplest window, equivalent to replacing all but N values of a data sequence
by zeros, making it appear as though the waveform suddenly turns on and off.
1. W(n)=1
2.
𝑊
𝑅
(𝑛) =
1 𝑓𝑜𝑟 |𝑛| ≤ (𝑀−1)/2
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠e