Design 5 th order Linear Phase Low Pass FIR filter with wc = π3 using hammingwindow function

To design a 5th order Linear Phase Low Pass FIR filter with a cutoff frequency of wc = π/3 using the Hamming window function, follow these steps:

Step 1: Determine the filter length The filter length for a 5th order filter can be calculated using the formula: N = (order * 2) + 1 In this case, the order is 5, so the filter length is: N = (5 * 2) + 1 = 11

Step 2: Calculate the normalized cutoff frequency The normalized cutoff frequency is given by: wn = wc / (π/2) In this case, wc = π/3, so the normalized cutoff frequency is: wn = (π/3) / (π/2) = 2/3

Step 3: Generate the ideal impulse response The ideal impulse response for a low pass filter can be calculated using the formula: hd[n] = (wn / π) * sin(wn * (n - (N-1)/2)) / (wn * (n - (N-1)/2)) where n is the index of the sample, and N is the filter length.

Step 4: Apply the Hamming window function The Hamming window function can be calculated using the formula: w[n] = 0.54 - 0.46 * cos(2πn / (N-1)) where n is the index of the sample, and N is the filter length.

Step 5: Multiply the ideal impulse response with the Hamming window function To obtain the final filter coefficients, multiply the ideal impulse response (hd[n]) with the Hamming window function (w[n]) for each sample index n.

Step 6: Normalize the filter coefficients To ensure that the filter has unity gain at DC, divide all the filter coefficients by the sum of the coefficients.

Following these steps will allow you to design a 5th order Linear Phase Low Pass FIR filter with a cutoff frequency of wc = π/3 using the Hamming window function.