Resampling - Interpolation



Here we look at converting a signal to a higher sample rate using interpolation. This process interestingly involves simply 'zero stuffing' extra samples followed by a low pass filter with cutoff at the OLD Nyquist frequency. Naturally you are not going to get any wider bandwidth out of the signal, just change it's sample rate, even though the new sample rate can accomodate a wider bandwidth signal.

First lets observe the zero padding by setting the filter cutoff frequency too high: 

	sampling_freq = 4e6	# original signal at 4Msps

	fg = gr.flow_graph ()

	src = gr.sig_source_f ( sampling_freq, gr.GR_SIN_WAVE, \
		600e3, 1, 0 )		# 600Khz, amplitude 1, 0 offset
		
	# compute low pass filter taps - this time too high cutoff
	# to see the zero stuffing
	lpf_taps = gr.firdes.low_pass ( \
		1.0, 	# gain
		16e6, 	# new sampling rate, 4X old
		8e6,	# LPF cutoff at 8Mhz, too high
		500e3,	# transition band width
		gr.firdes.WIN_HAMMING )

	interp_filter = gr.interp_fir_filter_fff ( \
		4, 	# interpolation
		lpf_taps )

	dst1 = gr.file_sink (gr.sizeof_float, "signal_out")
	dst2 = gr.file_sink (gr.sizeof_float, "interp_out")

	fg.connect (src, dst1)		 # the original signal
	fg.connect (src, interp_filter)	
	fg.connect (interp_filter, dst2) # upsampled signal


Now lets look at the original signal:



which has about 6.666 points per cycle ( 4Mhz / 600Khz)
Next the upsampled signal with too high filter:



where you can clearly see 3 extra samples at zero between each of the original signal. Lastly we change the LPF cutoff to recreate the orignal signal at the new sampling rate. The original signal was sampled at 4Msps so we use 2Mhz: 

	lpf_taps = gr.firdes.low_pass ( \
		1.0, 	# gain
		16e6,	# new sampling rate, 4X old
		2e6,	# LPF cutoff at 2Mhz, just right
		500e3,	# transition band width
		gr.firdes.WIN_HAMMING )


and now you can see we have the original signal at the new sampling rate:



with 26.666 points / cycle ( 16Msps / 600Khz, or 4 * 6.6666 ).