Question

a. A notch filter is required to be designed, that produces a null at 5 kHz and unity gain at dc. The filter operates at a sampling frequency of 20 kHz. b. A continuous time signal is given to the input of the system in Figure . The signal is given as follows with $f_1$ = 10 kHz, $f_2$ = 20 kHz, and $f_3$ = 40 kHz: $x(t) = 2 cos(2pi f_1 t) - cos(2pi f_2 t) + frac{1}{2} cos(2pi f_3 t)$ i. Compute the resultant discrete-time signal? ii. Use the notch filter designed in part (a), as the LTI system, to process the input signal $x[n]$. iii. Construct the output $y(t)$, assuming ideal reconstruction. x(t) Ideal C-to-D Converter x[n] LTI System H(z) y[n] Ideal D-to-C Converter y(t) T = 1/f_s T = 1/f_s

          a. A notch filter is required to be designed, that produces a null at 5 kHz and unity gain at dc. The filter
operates at a sampling frequency of 20 kHz.
b. A continuous time signal is given to the input of the system in Figure . The signal is given as
follows with $f_1$ = 10 kHz, $f_2$ = 20 kHz, and $f_3$ = 40 kHz:
$x(t) = 2 cos(2pi f_1 t) - cos(2pi f_2 t) + frac{1}{2} cos(2pi f_3 t)$
i. Compute the resultant discrete-time signal?
ii. Use the notch filter designed in part (a), as the LTI system, to process the input signal $x[n]$.
iii. Construct the output $y(t)$, assuming ideal reconstruction.
x(t)
Ideal
C-to-D
Converter
x[n]
LTI
System
H(z)
y[n]
Ideal
D-to-C
Converter
y(t)
T = 1/f_s
T = 1/f_s

$a. A notch filter is required to be designed, that produces a null at 5 kHz and unity gain at dc. The filter operates at a sampling frequency of 20 kHz. b. A continuous time signal is given to the input of the system in Figure . The signal is given as follows with f1 = 10 kHz, f2 = 20 kHz, and f3 = 40 kHz: x(t) = 2 cos(2pi f1 t) - cos(2pi f2 t) + frac12 cos(2pi f3 t) i. Compute the resultant discrete-time signal? ii. Use the notch filter designed in part (a), as the LTI system, to process the input signal x[n]. iii. Construct the output y(t), assuming ideal reconstruction. x(t) Ideal C-to-D Converter x[n] LTI System H(z) y[n] Ideal D-to-C Converter y(t) T = 1/fs T = 1/fs$

Added by Alexander B.

Question

Please give Ace some feedback