EE123 Digital Signal Processing

Transcription

1 EE123 Digital Signal Processing Lecture 29 Lab 5 Part I 2D Signals and 2DFT

2 Announcements Frequency Measurement Challenge Due tonight! Project update meetings Teams and Projects proposals! Must meet me till next Wednesday Must meet JT, FO or ML every week Get audio interfaces for lab 5 I m monitoring SPLXCAL (ch4) or KB6LED (ch26) feel free to call

3 Lab 5 Part I Purpose is to make sure everything works with your audio interface. Tools for working with it Tools to test it

4 Audio Inteerface

5 Important information There s information on how to install, how to use, how to operate and how to debug. Please read carefully! We provide functions for buffered audio using threads and queues Threads are tricky! can not be killed Added queue to help terminate a thread through command

6 Audio Devices and USB There s instructions on how to find the audio device numbers These may change if there s apple TV on the network def printdevnumbers(p): N = p.get_device_count() for n in range(0,n): name = p.get_device_info_by_index(n).get('name') print n, name p = pyaudio.pyaudio() printdevnumbers(p) p.terminate() 0 Built-in Microph 1 Built-in Output 2 USB PnP Sound Device

7 Calibrate radio output/ computer input level We need to make sure you can record from the radio and that the audio is not clipped or distorted Record from the radio and play using computer speaker -- measure maximum signal and nrms

8 Make sure PTT control works well We use pyserial to control USB2Serial device to key the radio You need to find your device! This is the first point of failure when things can hang due to RF interference if sys.platform == 'darwin': # Mac s = serial.serial(port='/dev/tty.slab_usbtouart') else: # Windows s = serial.serial(port='com1') s.setdtr(0) for n in range(0,10): s.setdtr(1) time.sleep(0.25) s.setdtr(0) time.sleep(0.25)

9 Buffered Audio and Keying command You can issue key-on and key-off commands through the data pipeline. Easy to sync transmission and data Examples with and without threading Qout.put("KEYON") Qout.put(sig2) Qout.put("KEYOFF") Qout.put(sig2) Qout.put("KEYON") Qout.put(sig1) Qout.put("KEYOFF") Qout.put("EOT") # play audio from Queue play_audio(qout, cqout, p, fs_usb, dusb_out, s,0.2)

10 Calibrating audio level to radio Play from computer, transmit with radio, receive with SDR Pay attention to the instructions and tips! remove antenna from SDR, use low gain Play tone with increasing amplitude -- look at when it saturates

11 Calibrating audio level to radio Need to FM demodulate Lowpass, decimation, limiter, discriminator Look at the tone amplitude by envelope detection

12 Calibrating audio level to radio linear non-linear Find the gain that keeps you in the linear region.

13 Measuring the input frequency response for the radio Radio has band pass filter Also emphasizes high frequencies Two methods: Generate a chirp, transmit and recieve with SDR, demodulate and look at the response. Generate noise, transmit and recieve with SDR, demodulate and look at the average power spectrum

14 Response to chirp and noise

15 Response to Chirp and noise tones due to RF interference with audio interface

16 Write a Morse Code Function Transmit your call sign in morse code Useful for automatic identification later! def text2morse(text,fc,fs,dt): CODE = {'A': '.-', 'B': '-...', 'C': '-.-.', 'D': '-..', 'E': '.', 'F': '..-.', 'G': '--.', 'H': '...', 'I': '..', 'J': '.---', 'K': '-.-', 'L': '.-..', 'M': '--', 'N': '-.', 'O': '---', 'P': '.--.', 'Q': '--.-', 'R': '.-.', 'S': '...', 'T': '-', 'U': '..-', 'V': '...-', 'W': '.--', 'X': '-..-', 'Y': '-.--', 'Z': '--..', '0': '-----', '1': '.----', '2': '..---', '3': '...--', '4': '...-', '5': '...', '6': '-...', '7': '--...', '8': '---..', '9': '----.', ' ': ' ', "'": '.----.', '(': '-.--.-', ')': '-.--.-', ',': '--..--', '-': '-...-', '.': '.-.-.-', '/': '-..-.', ':': '---...', ';': '-.-.-.', '?': '..--..', '_': '..--.-' }

17 Multi-Dimensional Signals Our world is more complex than 1D Images: f(x,y) Videos: f(x,y,t) Dynamic 3D scenes: f(x,y,z,t) Medical Imaging 3D Video Computer Graphics We will focus on 2D

18 Continuous-Time 2D functions δ(x,y): Impulse at x=0, y=0 δ(x) : Impulse line (vertical or horizontal?) (x,y) : 2D rect function cos(2π(fxx + fyy)) - Spatial harmonic Circularly Symmetic: (x,y): Pillbox u(r) 1 2

19 Spatial Frequency What is a spatial frequency? Complex Harmonic: e j( xx+ y y) = e j2 (f xx+f y y) Units (for example): x,y - cm fx,fy - 1/cm Ωx, Ωy - rad/cm

20 Spatial Frequency Vinyl Record Transforms a temporal signal to a spatial signal

21 Spatial Frequency CD ROM encodes digital temporal signals to spatial signals

22 What is the frequency? (-1,1) sin(2 (f x x + f y y)) (1,1) (-1,-1) a) fx=2, fy=2 b) fx=1, fy=0 c) fx = 4, fy=0 (1,-1) d) none of the above (1,1)

23 What is the frequency? (-1,1) sin(2 (f x x + f y y)) (1,1) (-1,-1) (1,-1) 2 cycles for 2 cm fx=1 cm -1 (1,1)

24 What is the frequency? sin(2 (f x x + f y y)) (-1,1) or cos(2 (f x x + f y y)) (1,1) (-1,-1) a) sin, fx=0, fy=2 b) cos, fx=0, fy=4 (1,-1) c) cos, fx = 0, fy=2 d) none of the above (1,1)

25 What is the frequency? (-1,1) cos(2 (f x x + f y y)) (1,1) (-1,-1) a) fx=1, fy=2 b) fx=4, fy=2 c) fx = 2, fy=1 d) fx=2, fy=4 (1,-1) (1,1)

26 What is the frequency? (-1,1) cos(2 (f x x + f y y)) (1,1) (-1,-1) a) fx=1, fy=2 b) fx=4, fy=2 c) fx = 2, fy=1 d) fx=2, fy=4 (1,-1) (1,1)

27 What is the Temporal Frequency? Vinyl rotates at 1 Hz (-1,1) (1,1) (-1,-1) a) cos(2π8t) b) cos(2π8t 2 ) c) cos(2π4t) d) cos(2π4t 2 ) (1,-1) (1,1)

28 What is the Temporal Frequency? Vinyl rotates at 1 Hz (-1,1) (1,1) Aliasing! (-1,-1) a) cos(2π100t) b) cos(2π100t 2 ) c) cos(2π40t) (1,-1) d) none of the answers (1,1)

29 2D Fourier Transform F (f x,f y )= Z 1 1 Z 1 1 f(x, y)e j2 (f xx+f y y) dxdy

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32 sinc(ax)sinc(by)

33 sinc(ax)sinc(by)

34 2D DTFT F (! x,! y )= 1X 1X f[n x,n y ]e j(! xn x +! y n y ) n x = 1 n y = 1 apple! x,! y apple F (apple x, apple y )= I prefer 2nd 1X 1X n x = 1 n y = 1 f[n x,n y ]e j2 (apple xn x +apple y n y ) 0.5 apple apple x, apple y apple 0.5 Massaging the DTFT leads to separable transforms in each axis

35 2D - DFT Similarly to 1D: Forward: F [k x,k y ]= NX 1 MX 1 f[n x,n y ]e j2 (n xk x /N +n y k y /M ) n x =0 n y =0 apple x = k x /N, apple y = k y /M Inverse: f[n x,n y ]= 1 NM NX 1 k x =0 MX 1 k y =0 F [k x,k y ]e +j2 (n xk x /N +n y k y /M )

36 2D - DFT F [k x,k y ]= NX 1 MX 1 f[n x,n y ]e j2 (n xk x /N +n y k y /M ) n x =0 n y =0 M f[n x,n y ] F [k x,k y ] (0,M) ny ky (0,0) N nx (0,0) kx (N,0) Need to fftshift in 2D to get it to look like DTFT.

37 Properties of 2D DFT Circular Convolution f[n x,n y ] h[n x,n y ]=F [k x,k y ]H[k x,k y ] Circular shift f[(n x m x ) N, (n y m y ) M ]=e j2 (k xm x /N +k y m y /M ) F [k x,k y ]

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43 background: signal: e j2 k 0f =1 e j2 k0f +1 = ((e j2 k0f + 1)(e j2 k0f + 1)) 1/2 = (2+e j2 k0f + e j2 k0f ) 1/2 = (2 + 2 cos(2 k 0 f)) 1/2