Intro to DSP: Sampling. with GNU Radio Jeff Long

Transcription

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2 Intro to DSP: Sampling with GNU Radio Jeff Long

3 ADC SDR Hardware Reconfigurable Logic Front End Analog Bus USB2 USB3 GBE PCI Digital Data Control Analog Signals May include multiplesystem Typical SDR Radio frequency (over the air) Phases (I/Q or Quadrature) Baseband to ADC) (RX) Antennas (input (MIMO) Continuous Real Digital Signals Represent analog Discrete Evenly spaced in time (no two are alike) Travel in groups (DMA, buffers)

4 Start with something simple...

5 Linear motion sawtooth wave Constant speed periodic signal Known start time clock sync

6 Measure Analog (1,0,-1,0,1,0,-1,0,1) Continuous Signal Discreet Values t Δ Tsample Tsignal = 1 / Fsignal Constant Rate Clock (Fsample)

7 Nyquist Rate Fsample > 2 Fsignal MAX MIN Sampling Ratio = Fsample / Fsignal = Tsignal / Tsample

8 Δ t 1x 2x 4x

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10 2x sampling Time (Phase)ratio Shiftcannot represent phase t 2x Time is information!

11 Start ¼ period early (or late) Can we measure 2 signals with one value? Take advantage of phase different start times.

12 t

13 Fsample > 4 Fsignal I n phase S ignal Q uadrature S = I + jq 'j' means 90 out of phase t

14 RF communication is based on sine waves Sine and Cosine are the same function, shifted by 90 (π/2) Addition? Same function, shifted! sig1 = cos(x) sig2 = sin(x) (sig1 + sig2) * 1/ 2 Same frequency Different phases WHY? Frequency (FFT magnitude) Phase (FFT angle)

15 Adding Sines in the time domain is the same as adding impulses in the frequency domain Display using GNU Radio frequency sink A-major Chord 440 Hz 554 Hz 659 Hz 880 Hz Fsample = 4000 S/s

16 Sample rate = 4000 S/s can represent signal freq < 2000 Hz Hurts the ears 440 Hz 554 Hz 659 Hz 1000 Hz Fsample = 4000 S/s

17 Sample rate = 4000 S/s can represent signal freq < 2000 Hz 3120 Hz tone aliases down to 880 Hz from Second Nyquist Zone = 880 A-major Chord 440 Hz 554 Hz 659 Hz 880 Hz Fsample = 4000 S/s

18 Sine Wave Swept khz 1MS/s Keep 1 in 2 (Decimation) 500kS/s

19 Sine Wave Swept khz 1MS/s Keep 1 in 2 (Decimation) 500kS/s Both signal AND noise will be aliased another reason to filter.

20 Decimator Decimator Anti Aliasing Filter Downsampling = Filtering + Decimation

21 Interpolator Image Reject Filter Upsampling = Interpolation + Filtering

22 Clocking Complications No Clock Processor Audio * Clock Domains GNU Radio does not have its own clock (* exception) Device sources and sinks have clocks Usually different clocks creating clock domains Frequency tolerances Not synced (out of phase) Must pick a clock Usually only one good choice Audio drivers will often resample (ALSA plughw:1,0)

23 Clocking Domains No Clock Processor Audio BAD (with ALSA hw:) Processor and Audio both working off their own clocks Over/underruns, stutter GOOD (with ALSA plughw:) Audio driver does software resampling to match clocks

24 Clocking Complications RTL Clock USRP Clock BAD No good way to sync clocks Will see either OOOOOOOOOO RTL buffer overrun UUUUUUUUUU USRP buffer underrun

25 Clocking Domains BOTH GOOD Only one clock domain Rest of flowgraph will maintain pace

26 Buffers

27 ADC Buffer Block Handling one sample at a time is slow Many blocks require multiple samples Filter history FFT and other block operations SIMD optimization Add buffering, operate on batches of samples Improves performance Increases latency Hides rate mismatches for a short time Buffer

28 Block Block Buffer Block Buffer Buffer Buffers hold the output of each block. GR passes items between blocks, the most common being samples. Multiple blocks can read from the same buffer. Buffer Trivia

29 The Vertical

30 Clipping t Voltage limits Representation limits Analog circuitry Maximum value ADC settings Minimum resolution

31 Headroom Quantization Noise Signal Level Tradeoff t

32 Lower resolution or lower signal = More quantization noise t Can trade off oversampling (averaging) vs resolution 1 bit of resolution ~ 2x oversampling (*) depends on noise characteristics

33 Common GR Types Float32 (float): 23 bits (Complex is 2 floats) Integer8 (byte): 8 bits Integer16 (short): 16 bits Integer32 (int): 32 bits Sample Types One bit for +/-

34 Float/Complex Can scale to any useful range Often scaled to +/- 1.0 Signed Byte/Short/Int Have fixed range +/- 127 / 32K / 2G Short Float Float Short Sink expects Source produces ~ 1.0~ 1.0 Signal File willwill contain be clipped values near Scale 1.0 / or lower zero Scale or lower Sample Type Conversion

35 Sampling Window (Integration Time) t Due to capacitance in ADC Acts as a low-pass filter

36 What is the right rate? Real: > 2 * max signal frequency Quadrature: > 4 * max signal frequency Account for filter rolloff Oversample to reduce noise Oversample to relax filter quality requirements If aliasing is desired, undersampling is OK Hardware May not support arbitrary rates May have better quality rates Performance limits (sampler, bus, computer) Prescribed rates (LTE 10 MHz channel MS/s)

37 Isolate a signal from noise and other signals Perform anti-aliasing or image-rejection (rate change) GR filters can interpolate or decimate FAQ: Why do I get 'OOOOOOOO' with a simple flowgraph? Efficiency in filtering Use the cheapest filter that does the job right Downsample as early as possible, upsample late Use multiple stages for large rate changes 1MS/s, 100 Hz transition taps ~24 GFLOPS (using FIR) Some blocks contain filters, perform rate changes Filters

38 ADC???