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Amplitude Modulation Function
Syntax y = ammod(m,ka,fc,pc,fs)
Include: include spt\ammod.oms
See Also fmmod , pmmod , quadmod

ARGUMENTS:
   INPUTS:
      m  = MATRIX, any numerical type, coerced to DOUBLE for
           internal processing. Represents sampled version of an
           arbitrary baseband modulation waveform in [Volt].
      ka = SCALAR, any numerical type, coerced to DOUBLE for
           internal processing. Modulator sensitivity in [1/Volt].
           Scales 'm' before modulation. Typically 0.0 to 1.0.
      fc = SCALAR, any numerical type, coerced to DOUBLE for
           internal processing. Carrier frequency in [Hz].
      pc = SCALAR, any numerical type, coerced to DOUBLE for
           internal processing. Carrier phase in [radians].
      fs = SCALAR, any numerical type, coerced to DOUBLE for
           internal processing. Sampling rate in [Samples/sec].
   RETURN: MATRIX, type DOUBLE, sampled AM waveform. Same 
           dimensions as input 'm'.

Description

Sample a AM (Amplitude Modulation) modulated carrier with given baseband modulation waveform, carrier frequency and carrier phase in a column-wise fashion.

Returns a sampled version of a AM modulated carrier with the same dimensions as input 'm'. The user specifies the arbitrary baseband modulation waveform 'm' in [Volts], the sampling rate 'fs' in [Samples/sec], the carrier frequency in [Hz] 'fc', the carrier initial phase angle in [radians] 'pc', and the modulator sensitivity 'ka' in [1/Volt]. All inputs may be any numerical type and are coerced to DOUBLE for local processing.

The general form of the modeled AM waveform is:

           (1 + ka*m) % cos(2*PI*fc*t + pc),

and this waveform is sampled at a rate of 'fs'. The amplitude of the resulting carrier sinusoid is proportional waveform 'm'. 'm' may be a matrix, in which case an identically dimensioned matrix is returned where each column of 'm' has separately been modulated onto the specified carrier. The modulation sensitivity factor 'ka' scales the waveform 'm' before applying it to the carrier and typically has a value of 0.0 to 1.0 (though not restricted by the function). The user should note that if the quantity 'ka*m' is anywhere less than -1 then the waveform is said to be 'overmodulated', i.e., carrier phase reversals occur. This situation is allowed by the function and it is up to the user to suitably restrict the waveform 'm' as desired.

It should also be noted that the function places no restrictions on the relation between carrier, modulation, or sampling frequencies. The user may 'under-sample' the waveform by making the maximum frequency represented in 'm' or 'fc' higher than half the sampling rate without error. (This is in fact done deliberately in some sampled data systems).

Example

# Create a 100% AM modulated waveform

fs     = 256d0;          # sampling rate [Samples/second]
N      = 256;            # record length [Samples]
fc     =  32d0;          # carrier frequency [Hz]
pc     =   1d0;          # initial carrier phase [radians]
fm1    =   4d0;          # modulation freq [Hz]
twopit = 2d0*PI*(seq(N)-1d0)/fs; # Create 2*PI*time
m      = cos(twopit*fm1);        # Create modulation waveform
ka     = 1;               # Modulator Sensitivity, 1Volt/Volt
am     = ammod(m,ka,fc,pc,fs);  # Create the time waveform
spec   = abs(dft(complex(am))/N)^2d0; # Compute the spectrum power
amspec = spec.row(1,N/2+1); # Select first half of the spectrum
amspec = amspec + {0d0,reverse(spec.row(N/2+1,N/2))};
amspec = db10(amspec);                # spectrum mag, dB
t      = timeaxis(1d0/fs, N);         # time axis for plotting
f      = freqaxis(fs/N, N);           # freq axis for plotting

ginit;
format double "f7.1";
gaddtext("AM MODULATOR Function", [.5,.95]);
s=["fs =",ntoa(fs)," Hz"," , fc =",ntoa(int(fc))," Hz"," , fm =",ntoa(int(fm1))," Hz"];
gaddtext(s, [.5,.90]);

vp1 = gaddview(0.05, 0.50, .90, .35 );
gyaxis("linear",-2,2,2,2);
gxaxis("linear",0,N/fs,4,5);
gplot(t,am);
gxtitle("TIME");
gytitle("VOLTS");
gtitle("ammod() WAVEFORM");
gygrid("minor");
gxgrid("major");

vp2 = gaddview(.05, .05, .90, .35 );
gyaxis("linear",-20,0,4,2);
gxaxis("linear",0,fs/2,4,4);
gygrid("minor");
gxgrid("major");
gxtitle("FREQ");
gytitle("MAG [dB]");
gtitle("ammod() SPECTRUM");
gplot(f.row(1,N/2+1),amspec);

Reference

Haykin, Simon, "Communication Systems.", New York: Wiley, 1994 .