. Given the
following non-periodic signal:
x(t) = 3 e-5t cos(12t)
u(t)
Find the Fourier transform expression X(ω) without
using Table.
Calculate the magnitude spectrum of X(ω) for ω = π/8, π/4, and
π/2
Given a sinusoidal signal:
x(t) = Asin(2πft)
Find Fourier Transform (FT) of the sinusoidal x(t) given above
and plot the spectrum with:
a. A = 2, f = 1000Hz
b. A = 2, f = 9000Hz
c. A = 5, f = 1000Hz
d. A = 10, f = 10000Hz
One period of a real-time signal x(t) =2Sin(20*pi*t) , starting
at t=0, has to be processed in a 4-bit digital computer. The A/D
card have a sampling frequency of 55Hz and the input range is +/-
2Volts.
i) What are the values recorded in the sampled signal x[n] ?
ii)What is the resulting quantized signal?
iii)What is the resulting digitized/coded signal?
iv)If the sampled signal x[n] was filtered using a moving
average filter of length 3 , what would the...
use matlab
y(t)=10*(cos(2*pi*500*t)+cos(2*pi*1000*t)+
cos(2*pi*1500*t)).
e) Down sample y(t) by a factor of 6. Sketch the Fourier
transform with appropriate frequency axis. Check if all frequency
components are correct?
Up-sample the time-domain signal obtained in e) by a factor of
6. Use appropriate filter for interpolation. Sketch the Fourier
transform of the up-sampled and filtered signal. Does the resulting
signal show all frequency components of the original signal
y(t)?
use matlab
y(t)=10*(cos(2*pi*500*t)+cos(2*pi*1000*t)+
cos(2*pi*1500*t)).
e) Down sample y(t) by a factor of 6. Sketch the Fourier
transform with appropriate frequency axis. Check if all frequency
components are correct?
Up-sample the time-domain signal obtained in e) by a factor of
6. Use appropriate filter for interpolation. Sketch the Fourier
transform of the up-sampled and filtered signal. Does the resulting
signal show all frequency components of the original signal
y(t)?
Use for statements to find the values of x(t) = 3 cos (2?ft +
0.1) for t = 0,
01, 0.2, 0.3, 0.4 s when f =10, 15, and 20 Hz. Use one set
ofstatements to compute the values for all three frequencies and
store the results in a two-dimensional array. Use two nested for
loops and double indexing.
a) Let ?(?) = cos(2??) and ?(?) = cos(20??). Write the
mathematical expression for the Fourier transform of ?(?) = 4[1 +
0.5?(?)]?(?) as a function of both ? (rad/s) and ? (Hz) by hand.
Moreover, plot the magnitude spectrum of ?(?) by hand as functions
of both ? (rad/s) and ? (Hz).
b) By using a 2x1 subplot, plot ?(?) signal in the first row.
Take ? between -20 s and 20 s with an increment of 1 ms....
Find the Fourier Series for the function defined over -5 < x
< 5
f(x) = -2 when -5<x<0 and f(x) = 3 when 0<x<5
You can use either the real or complex form but must show
work.
Plot on Desmos the first 10 terms of the series along with the
original
function.