Final answer:
The impulse response h_1(t) for an ideal lowpass filter with the specified frequency response H_1(jω) is a sinc function given by h_1(t) = (1/πt) sin(525 × 2πt). The impulse response is obtained by taking the inverse Fourier transform of the frequency response.
Step-by-step explanation:
The student has asked for the impulse response <em>h_1(t)</em> for an ideal lowpass filter with a certain frequency response. The given frequency response <em>H_1(jω)</em> describes an ideal lowpass filter that allows frequencies up to 2π(525) rad/s and attenuates frequencies above that. The impulse response is obtained by taking the inverse Fourier transform of <em>H_1(jω)</em>. For an ideal lowpass filter with the given characteristics, the impulse response is a sinc function, which is given by:
h_1(t) = (1/πt) sin(525 × 2πt)
It is important to correctly apply the inverse Fourier transform to get the exact form of the impulse response, which in this case is band-limited due to the cutoff frequency at 2π(525) rad/s.