Due: 10 am, September 19 (Thursday).

In this week's lab, we will modulate a carrier wave with a PRN code sequence. In particular, we'll look at the signal in the frequency domain. This allows us to see the spread spectrum nature of the GPS signal. First, we need to know how to generate a sine wave, and compute the spectrum of this unmodulated carrier. This is the focus of this week's prelab. Note: this can be a stand-alone program - it does not have to be a function.

Most of you should you have learned rudimentary spectral analysis terms in ASEN 3300. Those who have not taken 3300 or a similar class can drop by my office for additional help.

Generate a sine wave and power spectrum of given characteristics:

• N: number of points: 2¹³
• T_s: sampling period: 0.001 seconds
• frequencies of the carrier signals (sine waves), F₁ = 50 Hz and F₂ = 10 Hz with amplitudes of 5 and 2, respectively.

Your program must follow these steps:

1. Define N
2. Define sampling period T_s (in seconds)
3. Define sampling frequency F_s = 1/T_s
4. Use N points and T_sto generate time signal starting from 0.
5. Define a sine wave function (SWF) using F₁ and F₂ (SWF = amplitude*sine(2*pi*time*freq)).
6. Plot the SWF in the time domain between 0 and 0.4 seconds.
7. Y = fft(SWF) computes the Fast Fourier Transform.
8. Ps = Y.*conj(Y)/N computes the power spectral density.
9. F = F_s*(0:N/2-1)/N creates the frequency axis, starting at zero and ending at the Nyquist frequency.
10. Plot frequency vs. power spectral density (Ps(1:N/2)). Don't worry about the y-axis units, but do define the x-axis units.