# spectrum representation

Discussion in 'Homework Help' started by jstrike21, Jan 27, 2010.

1. ### jstrike21 Thread Starter Member

Sep 24, 2009
104
0
x(t)= 10cos(800pi*t+pi/4)+7cos(1200pi*t-pi/3)-3cos(1600pi*t)

I have to sketch the spectrum of this signal, indicating the complex size of each frequency component. Then make seperate plots for real/imaginary or magnitude/phase of the complex amplitudes at each frequency

I have worked out:
x(t)= 5e^(jpi/4)e^(j800pi*t)+5e^(-jpi/4)e^(-j800pi*t)+3.5e^(-jpi/3)e^(j1200pi*t)+3.5e^(jpi/3)e^(-j1200pi*t) -1.5e^(j0)e^(j1600pi*t)-1.5e^(-j0)e^(-j1600pi*t)

I think this may be wrong could i get some assistance on this and A little explanation on what the bold part in the question means.

2. ### MasterSnow Member

Jan 18, 2009
22
0
You actually don't need to worry about breaking each sinusoid down into its complex exponential form. Since this signal is made up of nice, steady state sinusoids, you can use phasor analysis. ie Real(magnitude*e^(j*(frequency*t + phase))) = magnitude*cos(frequency*t + phase). What they mean by complex size is the magnitude and the phase angle together in an expression like magnitude*e^(j*phase). As you can see, you have three perfectly narrow frequencies in the signal, so your plot will contain three straight lines of varying magnitude depending on what you're representing. The bold part appears to mean that they want a plot that shows just the magntidue represented or just the phase represented.

Hope this helps!

3. ### jstrike21 Thread Starter Member

Sep 24, 2009
104
0
so i have Re(10e^(j400t)e^(j*pi/4)+7e^(j600t)e^(-j*pi/3)-3e^(j400t)e^(j*0)) is this correct?

4. ### jstrike21 Thread Starter Member

Sep 24, 2009
104
0
can anyone give confirmation?