(TCO 1) A signal given by 15 Cos (20t) 20 Sin (40t) is sampled at a rate of 15 Hz. Is the Nyquist theorem violated

Fs = 15 Hz > 12.7322 Hz

Hence, Nyquist theorem is NOT violated

Step-by-step explanation:

Given that;

a signal given by 15cos(20t) + 20sin(40t)

sampled at a rate of 15 Hz

Is the Nyquist theorem violated?

so;

from 15cos(20t) + 20sin(40t)

Freq F1 = 20/2π  Hz

F1 = 3.1830 Hz

and

Freq F2 = 40/2π

F2 = 6.3661 Hz

Now, Nyquist's rate FN ≥ 2 × F_max

FN ≥ 2 × 6.3661

FN ≥ 12.7322 Hz

Now our given signal was sampled at a rate of 15 Hz

so, Fs = 15 Hz > 12.7322 Hz

Hence, Nyquist theorem is NOT violated

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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