However, these tend to be bad choices for DDS applications. Values like 8MHz, 16MHz, and 25MHz are very common. ylabel ( 'Amplitude ' )Ĭlock sources like crystals and packaged oscillators generally come in nice integer values for ease of use. set_yticks () fft_index = int ( len ( df_fft ) / 2 ) # Half of the FFT output figure ( figsize = ( 12, 8 )) fft_index = int ( len ( df_fft ) / 2 ) # Half of the FFT outputĪx. (These are the large blue peaks on either side of bin 100000 in the plot below.)įig = plt. However, the most prominent tones in the undithered signal are reduced significantly by dithering. Dithering isn’t perfect - you can see a few places where the dithered and undithered signals overlap closely. The plot below shows the undithered signal (blue) overlaid with the dithered signal (orange). On average, you’re going to have fewer peaks besides your carrier tone in the output signal. Dithering allows you, instead, to distribute those errors more evenly throughout the noise of the signal by interrupting the regularity with which they occur. Do this often enough, and your quantization errors end up no longer being periodic. This causes a larger-than-anticipated shift in sin rom addressing, and a larger-than anticipated jump in the output of the sin rom. An ideal dithering signal will randomly increment the phase accumulator by an additional bit. These quantization errors show up in the output spectrum as spurious peaks!Ī phase dither serves to make these errors less periodic. This gets you a periodic waveform at the output, but it also makes the quantization errors periodic. A DDS operates by cycling through ROM values in a periodic fashion. You can see this error by examining the contents of the sin rom: as you get closer to the zero crossing point of the sine waveform, you’ll see large quantization errors in the outputs of the ROM. Since a DDS is a sampled system, it’s going to contain some quantization error. So, what’s going on here? Why does adding noise improve SFDR? A quick list comprehension can filter out those bins by magnitude for our observation: Just by looking at the FFT, we can see a number of bins popping up through the -90dB mark. generate_dds_spectrum () # Shortening the time domain plot so sine features are visible generate_dds_frame ( dither_output = False ) df_fft = dds. generate_phase_array ( tuning, ( 2 ** 20 )) df_phase = dds. Observe the following DDS example, where dithering has been turned off in the output waveform:`ĭds = DirectDigitalSynthesis ( 100000000, 32, 4096, 12 ) freq = 2822400 tuning = dds. However, it serves a very cool purpose in a DDS application. Signal wise, this dithering bitstream is just noise. That’s the purpose of the excitement with np.left_shift() - it’s moving the 1’s and 0’s created by randint() up to one position of significance less than the truncated phase register’s LSB. if you’re truncating your phase accumulator to 12 bits, then your dithered bits should be the 13th bit less than the MSB. The dithering stream is a random sequence of 1’s and 0’s at a bit significance one less than the truncation bit depth. right_shift ( dds_frame, shift ) # Apply sin rom with lambda function (phase-to-amplitude) left_shift ( dither, ( shift - 1 )) dds_frame = np. acc_depth - 1 mask = mask - ( 2 ** ( shift ) - 1 ) dds_frame = np.
""" # Programmatically generates mask to truncate all but most sig bits Def generate_dds_frame ( self, dither_output = True ): """ Returns dds sine output from stored values in self.phaseĭither_output - add phase dither to dds signal (default True)
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