This radians or hertz?

rob w

A simple enough question here, hope its in the right forum!

I have a question worded as this for college;

If a time domain signal x(t) = 3sin(400t)+ 9sin(200t + 0.2) can be represented in the frequency domain as X(400) = 3, X(200) = 9@0.2, X(w) = 0 for w not equal to (200,400)...... And so on!

My question is this, is the frequency of this signal measured in radians or hertz? I.e. the 200 and 400?

I'm pretty sure they are radians, if it was hertz it would be 2*pi*( freq in hz)

Is this right and always the case? Just want to be sure before I do my exams in January, it's a little niggling doubt that's annoying me!

Thanks

2011

rob w wrote: »

My question is this, is the frequency of this signal measured in radians or hertz? I.e. the 200 and 400?

Frequency is measured in Hertz

The frequency of the 1st voltage = 400/(2 x pi) =63.66 Hz
The frequency of the 2nd voltage = 200/(2 x pi) = 31.83 Hz

1 Hertz = 2 x pi radians per second

TheChizler

The argument of a sine or cosine or w/e should be the phase, which could be w (omega) times t, or 2*pi*f times t, or either plus some phase. In your example you give one of the sine arguments as being 400t, which would correspond to the former.

2011

2011 wrote: »

Frequency is measured in Hertz

I should have said that the frequency can be expressed in either Hz or rad/s

rob w

Thanks lads, appreciate the replies, just wanted to be sure!