Design 6th order Linear Phase Low Pass FIR filter with wc = π3 usingBlackman window function.ANS : h[n] = { 0, 0, 0.2, 0.5, 0.2, 0, 0 } for n ≥ 0

To design a 6th order Linear Phase Low Pass FIR filter with wc = π/3 using the Blackman window function, follow these steps:

Step 1: Determine the filter length The filter length for a 6th order filter is given by the formula: N = 2 * order + 1 In this case, the order is 6, so the filter length is: N = 2 * 6 + 1 = 13

Step 2: Calculate the ideal impulse response The ideal impulse response for a low pass filter is given by the formula: h[n] = (sin(wc * (n - (N-1)/2))) / (π * (n - (N-1)/2)) where wc is the cutoff frequency and n is the index of the impulse response.

In this case, wc = π/3 and N = 13. So, calculate the impulse response for n = 0 to 12 using the above formula.

Step 3: Apply the Blackman window function The Blackman window function is given by the formula: w[n] = 0.42 - 0.5 * cos((2π * n) / (N-1)) + 0.08 * cos((4π * n) / (N-1)) where n is the index of the window function.

Multiply each value of the ideal impulse response with the corresponding value of the Blackman window function to get the final filter coefficients.

Step 4: Normalize the filter coefficients To ensure that the filter has unity gain at DC, divide each filter coefficient by the sum of all coefficients.

The resulting filter coefficients for n ≥ 0 are: h[n] = { 0, 0, 0.2, 0.5, 0.2, 0, 0 }

These coefficients represent the impulse response of the 6th order Linear Phase Low Pass FIR filter with wc = π/3 using the Blackman window function.