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tinuous-time signal xa(t) is composed of a linear combination of sinusoidal signals of frequencies F1 Hz, F2 Hz, F3 Hz, and F4 Hz. The signal xa(t) is sampled at a 10-kHz rate, and the sampled sequence is then passed through an ideal lowpass filter with a cutoff frequency of 4 kHz, generating a continuous-time signal ya(t) composed of three sinusoidal signals of frequencies 350 Hz, 575 Hz, and 815 Hz, respectively. What are the possible values of F1, F2, F3, and F4? Is your answer unique? If not, indicate another set of possible values of these frequencies.

          tinuous-time signal xa(t) is composed of a linear combination of sinusoidal signals of frequencies F1 Hz, F2 Hz, F3 Hz, and F4 Hz. The signal xa(t) is sampled at a 10-kHz rate, and the sampled sequence is then passed through an ideal lowpass filter with a cutoff frequency of 4 kHz, generating a continuous-time signal ya(t) composed of three sinusoidal signals of frequencies 350 Hz, 575 Hz, and 815 Hz, respectively. What are the possible values of F1, F2, F3, and F4? Is your answer unique? If not, indicate another set of possible values of these frequencies.

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University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Adi S

05/06/2024

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The continuous-time signal \( x_a(t) \) is sampled at a rate of 10 kHz. According to the Nyquist theorem, to avoid aliasing, the highest frequency component in \( x_a(t) \) must be less than half the sampling rate, which is 5 kHz (10 kHz / 2). Show more…

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tinuous-time signal xa(t) is composed of a linear combination of sinusoidal signals of frequencies F1 Hz, F2 Hz, F3 Hz, and F4 Hz. The signal xa(t) is sampled at a 10-kHz rate, and the sampled sequence is then passed through an ideal lowpass filter with a cutoff frequency of 4 kHz, generating a continuous-time signal ya(t) composed of three sinusoidal signals of frequencies 350 Hz, 575 Hz, and 815 Hz, respectively. What are the possible values of F1, F2, F3, and F4? Is your answer unique? If not, indicate another set of possible values of these frequencies.

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00:01 The frequency components of the signal that is x, a, t is shown below.

00:29 So, for f, m1 is equal to 300 hz, f, m2 is equal to 1200 hz, f, m3 is equal to 2150 hz and f, m4 is equal to 3500 hz.

01:14 The signal xa into t sampling frequency fs is equal to 2000 hz.

01:22 Fs, fs is equal to 2000 hz.

01:29 The idea low pass filter cutoff frequency fc is equal to 900 hz and that is low pass filter cutoff frequency.

01:43 And consider the frequency component.

01:47 Fmt is equal to 300 hz.

01:51 So, fs minus f1 is equal to 2000 hz minus 300 hz is equal to 1700 hz.

02:06 And the next one is fs plus fm1.

02:10 Fs plus fm1 is equal to 2000 hz plus 300 hz is equal to 2300 hz.

02:24 And the next one is 2fs minus fm1 is equal to 4000 plus 2000 is 1 fs value.

02:39 Hertz minus 300 hertz is equal to 3700 hertz.

02:48 And the next one is 2fs plus fm1.

02:53 2fs plus fm1 is equal to 4000 hertz plus 300 hertz is equal to 4300 hertz.

03:09 Consider the frequency component fm2 is equal to 500 hz.

03:16 So fs minus fm2 is equal to 2000 hz minus 500 hz is equal to 1500 hz.

03:31 And the next is fs plus fm2 is equal to 2000 hz plus 500 hz is equal to 2500 hz...

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