Period of signal

**jordanrs** · October 21st 2010, 04:45 AM

Stuck on the following problem, aint sure how to work out the signal of a composed sinusoid

given that $x(t) = cos(600\pi t)$ and $m(t) = 4 + 3cos(20\pi t)$ what is the period (if any) of the resulting signal

Also the signal $x(t) = 10cos(600\pi t + \frac{\pi}{3}) + 6cos(900\pi t - \frac{\pi}{4}) - 4cos(1500\pi t)$ whats the period of the signal

Im not sure how to calculate the period when theres more than one sinusoid wave

Any help most appreciated

**CaptainBlack** · October 21st 2010, 05:44 AM

Originally Posted by jordanrs

Stuck on the following problem, aint sure how to work out the signal of a composed sinusoid

Also the signal $x(t) = 10cos(600\pi t + \frac{\pi}{3}) 6cos(900\pi t - \frac{\pi}{4}) - 4cos(1500\pi t)$ whats the period of the signal

Im not sure how to calculate the period when theres more than one sinusoid wave

Any help most appreciated

First question snipped as it not complete.

The product of two sinusoids has sinusoidal components at the sum and diffrence frequencies. This for some amplitudes (non-zero) and phases is:

$x(t)=A\sin(300\pi t+\phi_1)+B\sin(1500\pi t+\phi_2)$

and since the larger period is an integer multiple of the smaller the final period is $1/150$ s

CB

**jordanrs** · October 22nd 2010, 02:45 AM

Originally Posted by jordanrs

Stuck on the following problem, aint sure how to work out the signal of a composed sinusoid

given that $x(t) = cos(600\pi t)$ and $m(t) = 4 + 3cos(20\pi t)$ what is the period (if any) of the resulting signal

Also the signal $x(t) = 10cos(600\pi t + \frac{\pi}{3}) 6cos(900\pi t - \frac{\pi}{4}) - 4cos(1500\pi t)$ whats the period of the signal

Im not sure how to calculate the period when theres more than one sinusoid wave

Any help most appreciated

cheers for your reply, the first part should have read

when $y(t) = x(t)m(t)$ and $x(t) = cos(600\pi t)$ and $m(t) = 4 + 3cos(20\pi t)$ what is the resulting period of $(y(t))$

also i still dont get how to calculate the periodm i dont see where you got 1/150 s from

**CaptainBlack** · October 22nd 2010, 08:27 PM

Originally Posted by jordanrs

cheers for your reply, the first part should have read

when $y(t) = x(t)m(t)$ and $x(t) = cos(600\pi t)$ and $m(t) = 4 + 3cos(20\pi t)$ what is the resulting period of $(y(t))$

also i still dont get how to calculate the periodm i dont see where you got 1/150 s from

You decompose the signal into a sum of sinusoids, then the period is the lcm of the individual periods of the components.

CB

Thread: Period of signal

LinkBack

Thread Tools

Display

Period of signal

Similar Math Help Forum Discussions

Periodic signal

[SOLVED] Future value annuities with a different payment period to the compounding period.

Signal Recovery

elementary signal help please!

Reconstruction of a quantizied signal. (Signal Theory & Sampling)

Search Tags