Given sinusoidal signals at frequency f and sampled at a fre

Given: sinusoidal signals at frequency, f, and sampled at a frequency, fs:

i. f = 60 Hz, fs = 80 Hz

ii. f = 1.2 kHz, fs = 3 kHz

iii. f = 10 Hz, fs = 8 Hz

iv. f = 16 Hz, fs = 10 Hz

For each of the above cases, find:

a. alias frequency that results for a sinusoidal oscillation at frequency, f, when the sampling rate is fs.

b. frequency resolution at this sampling rate if the sample length, N, has 1000 samples

c. cutoff frequency for the anti-aliasing filter

Solution

(A)

we are given to find alias frequncy

we will use formula to find alias frequency

alias frequency=|fs-f| or fs+f

(i)

We are given

f=60hz and fs=80hz

alias frequency=|fs-F|

alias frequency=80-60

alias frequency=20hz........Answer

alias frequency=fs+F

alias frequency=80+60

alias frequency=140hz........Answer

(ii)

We are given

f=1.2khz and fs=3khz

alias frequency=|fs-F|

alias frequency=|3-1.2|

alias frequency=1.8khz........Answer

alias frequency=fs+F

alias frequency=3+1.2

alias frequency=4.2khz........Answer

(iii)

We are given

f=10hz and fs=8hz

alias frequency=|fs-F|

alias frequency=|8-10|

alias frequency=2hz........Answer

alias frequency=fs+F

alias frequency=10+8

alias frequency=18hz........Answer

(iv)

We are given

f=16hz and fs=10hz

alias frequency=|fs-F|

alias frequency=|16-10|

alias frequency=6hz........Answer

alias frequency=fs+F

alias frequency=10+16

alias frequency=26hz........Answer