Clipping a sine wave
Clipping a sine wave (especially at the a/d
converter) will create harmonics and intermods. To show what occurs a
model was made with:
The plots show the clipped sine wave
results (.ps) (.pdf):
- complex sine wave with 16 cycles in 4096 points.
- noise added to sine wave 1e-9 of amplitude of sine wave
- sine wave is clipped at 70% of maximum/minimum. This is done for
real,imaginary and then just for real.
- DC offsets of about .1% are added to the signal.
The table below shows the amplitudes of the first harmonic on the left
(+5th) and first negative (-3rd) for +/- clipping of the amplitude with
no dc offsets (the red plots)
- Page 1: time domain samples. top real samples, bottom imaginary
samples. Horizontal offsets have been added for display puroses.
- black: no clipping
- red: clip positive,
negative amplitudes to +/- .7
- green: clip the
real single to +/- .7 .
- blue: clip
+/- amplitudes. Add .1% dc offset to both real and imaginary.
- purple: clip +/-
amplitudes. Add .1% dc to real and -.2% dc to imaginary
- Page 2: spectra:
- The vertical dotted green lines are every 16 cycles (the period
of the sine wave).
- top: the spectra without any clipping.
- There is 1 spike at 16 cycles.
- 2nd: clip sine to
- for a single rectangle harmonics would appear at 1,3,5,7,9
- When clipping both the positive and negative peaks of a sine
wave, you get 2 rectangles for each period of the sine wave, it's just
that one is inverted. Since the rectangles occur twice as often they
are spread twice as far in the frequency domain: 1,5,9...
- 3rd: Clip
just the real signal to +/- 7.
- The I,Q phase is now lost for the clipping (real but not
imaginary clipped) so we get an image in the other side.
- They now occur at 1,3,5,7
- 4th: Add .1% to
each clipped sine wave.
- We now get mixing products between dc and the sine wave. The
appear on both side of the sine wave spaced by the sine wave frequency.
- 5th: Add .1% dc
to real, -.2% dc to imaginary.
- There is now an asymmetry between real and imaginary so we
get an image in the other side. They show up at -1, +3...
- Page 3: Blowup of spectra showing amplitudes of spikes.
- this is the same as page 2 but I've blown up the vertical scale
so you can see how large the spikes are: