a$)$ Design a linear phase, causal, digital Lowpass FIR filter by using the windowing method $($use Hamming window$)$ that meets the following specifications with the lowest possible filter length, M:

Sampling frequency, $F_s=20kHz,$

Passband frequency, ${}_P=23000,ra\frac{d}{sec},$

Stopband frequency, ${}_{ST}=24000ra\frac{d}{sec},$

Minimum stopband attenuation $=40dB.$

Write down the resulting impulse response equation for the FIR filter, $h(n),$ in closed form.

$(15$ Points$)$