A continuous-time signal is given by, x(t) = cos (250 pi t) + 2cos(400 pi t) +4

Question

A continuous-time signal is given by, x(t) = cos (250 pi t) + 2cos(400 pi t) +4 cos (6000 pi t) + 4 cos(5000 pi t). a) Find the Nyquist sampling rate for no aliasing. b) Choose sampling frequency (f_s) as 2-times the Nyquist rate found in part-a. Find x(n) and its period, N. c) Use the sampling frequency found in part-b to design a non-recursive (FIR) digital filter using windowing functions such that the two smaller frequencies are suppressed with a minimum attenuation of -45dB while the two higher frequencies are passed. Transition width should be at least 300 Hz. Find a general expression for the coefficients of the FIR filter impulse response h(n) that meets the requirements by selecting appropriate window function, filter length (=N) and cut-off frequency. The final filter h(n) should be causal.

Explanation / Answer

a)For no aliasing condition

fs=2fm

according to question fm=3000Hz (maximum frequency of the signal)

fs=2*3000 = 6000Hz

Nyquist sampling rate = 1/2fm = (1/6000) seconds

b)Nyquist rate fs=2fm = 6000Hz

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.