1)Amplitude modulation. 2) Negative amplitudes in the signal??

      I studied about AM before 6 months, I believe. When I studied that I got some doubt. How do you say AM takes twice the bandwidth of the signal bandwidth. I tried everything to understand that but I couldn't. I have started using MATLAB about 2 or 3 ago and now I could understand many things. Now there is another doubt that I have.
Today I did this. 
1) I recorded my voice using wavrecord. It is in the variable y.
2) Then I plotted y.
      I later found that the variable 'y' has negative amplitudes too.
How do you get negative amplitudes?( I never knew that before!) 
Also I want to understand my first question,(i.e. AM has twice the BW of the signal BW) through simulation. If you write the code and post it, I would be much obliged.

Thanks in advance and I thank MATLAB for helping me understand the concepts.

[Daniel Shub]

Those who choose to answer questions generally do not just write code and post it. It is better if you show what you have done to investigate the BW of amplitude modulation and then ask a specific MATLAB question.

Answer 1

[Wayne King]

The Fourier transform of any real-valued signal is conjugate symmetric, in other words, the Fourier transform at -f is the complex conjugate of the Fourier transform at +f. If you have a signal that is zero for all negative frequencies in the Fourier domain that means either you have a signal that is not real-valued, or you have a signal that is identically zero.

[i Venky]

Thanks for answering my questions.

:)--

Answer 2

[Wayne King]

Hi, It is very common for any signal to have negative and positive amplitudes, particularly for signals that oscillate. If you take a signal with zero mean then the amplitudes oscillate around zero.

t = linspace(0,1,1e3);
x = cos(2*pi*100*t);
plot(t,x);

If you apply a DC shift to that signal of course the signal still oscillates, but now it may not have negative amplitudes.

x1 = 3+cos(2*pi*100*t);
plot(t,x1);

When you recorded your voice, the sound pressure variations in your voice cause the microphone diaphragm to vibrate. These vibrations are transduced into an oscillating voltage. So it is not surprising that these oscillations go positive and negative. Say from -2 to 2 volts.

There are several AM modulation schemes and you cannot say that it always doubles the bandwidth. For example, take the simple case of double sideband sinusoidal AM. Amplitude modulate a 100-Hz sine wave with a 20-Hz sinewave.

t = linspace(0,1,1e3);
y = (1+cos(2*pi*20*t)).*cos(2*pi*100*t);

If you look at the spectrum, the bandwidth only increases 40 Hz. It goes from 200 Hz wide (with line components at -100 and 100 Hz), to 240 Hz wide with an extra 20-Hz component below -100 and one above 100.

[i Venky]

The value of the voltage seems to be the same on both positive and negative side. Why is that so?

I wasn't talking about the other forms of AM. I was just talking about the basic AM.

Thanks

Answer 3

[Wayne King]

Just like what you see in a cosine or sine, as the phase changes through a cycle of 2*pi radians, those functions have equal positive and negative values. They are positive for 1/2 cycle and negative for 1/2 cycle.

"I wasn't talking about the other forms of AM. I was just talking about the basic AM."

What I have shown you is arguably the basic AM. Perhaps you should write an example signal.

Answer 4

[i Venky]

 I have another doubt too (that I got before 6 months). How can frequency be negative? I mean how can you say "the no of oscillations per second" to be negative?

[i Venky]

But the spectrum has frequencies in both positive as well as negative sides....

Answer 5

[i Venky]

To find the spectrum of the signal is there any other method apart from fft()?

[Wayne King]

fft() implements the discrete Fourier transform so if you have a N-point data vector, then the DFT is the Fourier transform applicable to those signals. If you are asking whether there are other convenient tools in MATLAB for getting the spectrum, then yes, in the Signal Processing Toolbox there are many. If you have a symbolic expression of a continuous time signal, you can use fourier() to implement the Fourier integral