Plot the magnitude response function normalized frequency

Solved Step by Step With Explanation-FIR Filter Coefficients and Implementation

Questions

(i) Form an expression for the transfer function of the filter, H(w), in terms of the coefficients.

(ii) With justification, determine whether or not this FIR filter has linear phase.

Answer

(i) The transfer function of a digital FIR filter can be expressed in terms of its coefficients as follows:

(ii) To determine if the FIR filter has linear phase, we need to check if the coefficients satisfy the condition for linear phase filters. A filter has linear phase if the coefficients are symmetric or anti-symmetric, meaning b0 = b-1 and b1 = -b-1.

In this case, you mentioned that bo and b1 are real and non-zero. If bo = 3/8 and b1 = 1/8, it does not satisfy the condition for linear phase because b0 and b1 are not equal. Therefore, this FIR filter does not have linear phase.

(-) (×) (-)

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| (b1) |

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(+) represents addition.

(×) represents multiplication.

|H(w)| = |3/8 + 1/8 * e^(-jw) + 1/8 * e^(jw)|

Now, plot the magnitude response as a function of normalized frequency w. The type of FIR filter can be determined based on the characteristics of the magnitude response. Depending on the specific shape of the response, it could be a low-pass, high-pass, band-pass, or band-stop filter. You'll need to evaluate the shape of the magnitude response to determine the type of the filter.