PC-Sonar User Guide
Contents
1. 6 5m distance is opened such that it gives a good echo and a small rule is held at a distance of 1 m The peak at 4 1 08m is the hand of the author and the peak at 0 8m is groundreflection from the floor All other smaller 3 echoes are from unknown sources Everything beyond 6m is from multiple reflections 4 5 3 5 3 distance m In addition to the basic control by keypresses a press of m or M toggles the display mode between static display and dynamic display of changes The Mathematics of the Chirp Sonar The Chirp The phase of a constant carrier is a linear function of time t O of The phase of a linear chirp is a quadratic function of time t a tt gqf The generated complex signal is given by x exp i The Transmitted and the Received Signal Only the real part of the generated signal x 1s sent The signal propagates through the air at the soundspeed c The propagation path may be s Then the signal is received after a pathdelay of At s c The imaginary part of the received signal is reconstructed from the received real part but with negative sign This complex signal is the complex conjugate of x t At y conj x t Ad The Chirp Sonar Algorithm z xy expli t q f exp t A q t At exp i wo At q A 2g Att Separation of the constant factor a exp i At q Af and replacement of At by 4t s c leads to z a expG Qt with Q 2q s c Thus z is a wave of2. If there are targets beyond the range their distance is estimated to real distance modulo actual range setting The speaker transmits a tone with raising frequency starting at f7 and ending at f2 This is a socalled chirp The length of the chirp is twice the time the sound needs to reach the range The signal received by the microphone has a propagation delay proportional to the distance of the reflecting target Therefore the reflected signal has a lower frequency than the actual frequency of the chirp The frequency difference 1s proportional to the distance of the target The edge frequencies f7 and f2 should be chosen sonar Parameters Sele as large as possible because targets can be detected LL A only if they are larger than the wavelength of the frequency which is given by the quotient speed of range m 8 sound in air frequency Itis 3 5 cm at 10 kHz On the other hand the resolution is proportional to the air temperature C difference of both edge frequencies low frequency edge Hz high frequency edge Hz The received signal is shifted to baseband using the chirp as the carrier This maps the frequency differences to absolute frequencies The spectrum of the baseband signal is displayed using the distance of the targets as the abscissa ChirpSonar by DJ5HG 3 See ees The chirp sonar scan to the left shows NGM k AQCde4 B 08 00 Chirp SONAR Echo Amplitude over Distance the author S office A door at about
3. Thus the phase y At s c of z is proportional to the length of the propagation path s Therefore the distance can be computed by s c w w The main problem is that the phase only 1s known modulo 22 This makes it necessary to start at zero distance and to move slowly to any other distance such that the phase is a continuous function of time The Implementation The signal processing loop of the Matlab program directly follows the above algorithm But of course it adds some technical features for a communication with the soundcard b noise reduction by a multirate lowpass filter c accumulating the phase d graphical output The main parts of the above algoritm are highlighted in the following signal processing loop of the program by yellow background The signal processing loop of the Matlab program one carrier is as follows while run rxs getdata ai blk wait for blk input samples putdata ao txs g Output Chirp data rst rxs ndtl blk state of real shift filter for k l1 n simple multirate lowpass filter x k 1 0 5 x k 1 2 end 1 0 25 xs k x k 2 2 end 2 x k 2 2 end xs k x k end save last sample for next loop cycle end if cnt lt 3 3 frames to set the starting position sp 0 6 start with zero phase sum else dp p 1p phase motion since last block if dp gt pi only pi lt dp lt pi allowed dp dp 2 pi elseif dp lt pi dp dp 2 pi end sp sp dp
4. E NEN Sir YOSIN V K AAT SANY 4 AK Fata ied Nf WA j The window named Position Sonar displays the spacial room of the experiment There are two markers at the top which correspond to the speakers The white grid defines the room coordinates in meters All peaks of the other figure are shown here as arcs around the speakers with the corresponding distance as their radius The luminosity is the product of both correlation signals Possible positions of the microphone are colored red A low base distance of the two speakers leads to a considerable angular uncertainty while the radial distance is well defined see upper figure The calibration of the distance as described above must be done individually for the left speaker and the right speaker In addition to the basic control by keypresses a press of b or B pops up displays with the actual binary Hadamard codes The technical implementation is the same as in the code sonar But two different codes with similar lengths are used on the two speakers and the receiver correlates with these two codes to get the two different distances
5. angular velocity Q which is proportional to the length of the propagation path s Therefore the spectrum of z indicates all targets by corresponding peaks The angular velocities of the spectrum only must be mapped to distances by s cQ 2q The Implementation The signal processing loop of the Matlab program directly follows the above algorithm But of course it adds some technical features for a communication with the soundcard b calibration of the timing between input and output c noise reduction by a highpass filter d noise reduction by a pulse blanker e graphical output The main parts of the above algoritm are highlighted in the following signal processing loop of the program by yellow background while run cnt cnt 1 rxsig getdata ai n wait for n input samples putdata ao txdat 6 output chirp data 6 distance calibration rxsig rxsig shiftindex end 1 shiftindex 1 high pass filter rxh hps filter hp 1 rxsig hps 0 noise blanker st std rxh standard deviation of signal if clir cnt lt 10 mst st clr 0 else mst relax st l relax mst 6 Simple IIR filter for standard deviation end rxh abs rxh gt 3 mst 0 6 blank all samples gt 3 standard deviation Hilbert filter rst rxh ndtl1 n state of real shift filter shift to baseband wrlps filter b a v lps lowpass filter distance iE clr ym yd yr actu
6. between detected targets are precise The absolute distance must be calibrated once after start of the program This is done the same way in all experiments a Select the window of the desired sonar b Fix a target at a known distance from the left speaker such that it causes a clear peak c Now click with the mouse on the peak drag the mouse while pressing the mouse to the correct position on the horizontal distance scale d Release the mouse button The peak should move now to the new position This procedure can be repeated whenever you want but a single calibration should be sufficient Also a basic control by key presses is common to all sonars A press of c or C clears the history of the averaging process A press of s or S stops the sonar application The figures remain on the screen Speed of 5 i peed of Sound Distances measured by a sonar are proportional to the speed of the sound It is dependent on the air temperature as shown here Therefore the parameter air temperature should be specified in the four experiments to improve precision Especially the CW sonar sees temperature differences as low as 0 5 C over a distance of 5 m D p e uw Uj D T fab wm DL uw 0 10 20 air temperature C 4 1 Chirp Sonar The chirp sonar determines the distance of targets from the microphone and the left speaker which are assumed to be at the same location The range may arbitrarily be chosen
7. sum of phase motions since program start end d sp cs 2 pi fc actual distance between speaker and microphone lp p save actual phase oe cnt cnt 1 block counter if get ai SamplesAvailable lt blk set ith steang num2str d 8 4f m amp update distance amp max abs x n 1 scaling factor set lh XData 0 real x n 1 amp 0 YData 0 imag x n 1 amp 0 graphic end Colored words are while key words of the Matlab languge filter standard functions of Matlab including the Signal Processing Toolbox lt FET comments Program specific objects and variables are in black They are declared outside of this central loop 4 4 Position Sonar This sonar determines the position of the mono microphone in the plane defined by the microphone and the two stereo speakers Sonar Parameters Both speakers transmit different Hadamard codes modulated on the same carrier frequency The signal received by the microphone is correlated with both codes These correlation signals are displayed in the window named Correlation Signals The red and green lines horizontally show the distance between the microphone and the left resp the right speaker i iew Insert Tools Desktop Window Help OUSGWAas Fk ARVO L AO0E sa Position Sonar sample rate carrier frequency Baud rate range L R speaker distance fv A r Fak A 5 fN E i 4 JN A A a AN mm AR
8. PC Sonar User Guide Klaus von der Heide DJSHG 1 General PC Sonar is a program running on a PC with soundcard plus speaker and microphone It allows some simple sonar experiments without additional hardware The program is written in Matlab It is compiled by the Matlab Compiler 2 Requirements a Torun the program pcsonarexe the Matlab Compiler Rumtime MCR must be installed b pcsonar exe runs on all Windows systems later than Win98 and on 32 bit and 64 bit versions c The soundcard must support the samplerate 48000 d The sampling of sound output and sound input must be coherent 1 e the samplerates must exactly be the same If different soundcards are used for input and output this is not the case But even the same soundcard sometimes uses different rates for input and output 3 The Main Window PCSonar by DJSHG EAR PC Sonar starts with a simple window which allows selection of the desired experiment Pushing the help button to the right of an Sonar Type option displays specific help chirp help code help W help 2Dcode help 4 The Sonar Types PC Sonar supports four different sonar experiments which are explained in the following chapters All these experiments have one feature in common Unfortunately the sound input and output usually cannot be started precisely enough This leads to a considerable uncertainty of the delay between outgoing and incoming samples Therefore only relative distances
9. al echo clr 0 else end O o Scaling scl 1 mean ym mxy max ym if scl mxy gt 5 scl 5 mxy end display if mde set 1s XData 1 length ym m pro bin YData scl yd tyr ym update difference else set ls XData 1 length ym m pro bin YData scl ym update mean echo end end Colored words are while key words of the Matlab languge filter standard functions of Matlab including the Signal Processing Toolbox O O FFT comments Program specific objects and variables are in black They are declared outside of this central loop 4 2 Code Sonar This sonar determines the distance of targets from the microphone and the left speaker which are assumed to be at the same location The speaker transmits a sequence of bits modulated on the carrier according to your choice The length of this sequence is determined from the parameter minrange As in a radar system it is assumed here that the receiver the microphone cannot listen at its intrinsic sensitivity while the transmitter is sending Although other than in a radar system different antennas the speaker and the microphone are used we introduce this parameter minrange to specify the length of the code sequence The code is chosen such that it has small autocorrelation If minrange maxrange Hadamard codes are used because of their optimal properties in that special case of permanent transmission Sonar Parameters Se fx c
10. arrier frequency Hz 12000 v bitrate 1 s 12000 v modulation PSK The signal received by the microphone is correlated with the transmitted code This correlation signal is displayed over the distance of targets leading to peaks in this diagram To the left the echo of two nner buildings at a Daum 9 Of distance slightly larger than 150 m from the author s home Code SONAR o b a E o oO o In addition to the basic control by keypresses a press of b or B pops up a display with the actual binary code The signal processing loop of the Matlab program is as follows while run 6 sampling Putdata a0 Cxsiq OUTLPUL TX Signal rxs getdata ai cycl 6 wait for cycle input samples o0 6 Hilbert filter rst rxs ndtlicycl state of real shift filter lt shift to baseband decimation 1 74 xl ips talter 15 1 1ps decimation filter xd x1 1 4 end decimation lt COrrelaclion Lt nba iz mode case of PSK modulation o0 case of ASK modulation ax abs xd 6 signal amplitude ax ax mean ax signal deviation from mean y Crs tilter cdr 1 ax crs lt correlation filter yd abs y end else yd abs xd case of single pulse end distance calibration yd yd shiftindex end 1 shiftindex 1 rotate vector by shiftindex graphic 1 I Clr ym relax yd Clear mean echo clr 0 else ym rel
11. ax yd l relax ym simple IIR filter end yym max ym set lm YData ym yym update graphic of echo end while run Colored words are while key words of the Matlab languge filter standard functions of Matlab including the Signal Processing Toolbox lt FFT comments Program specific objects and variables are in black They are declared outside of this central loop 4 3 CW Sonar This is a high precision sonar which determines the distance of the mono microphone from the left speaker at an accuracy better than one millimeter The principle is simple The speaker transmits a continuous wave of frequency f0 The phase difference between transmitted and received waves is determined and transformed to distance The distance is displayed numerically and graphically by a rotating pointer The zero distance must be calibrated This is done by starting the program with the microphone at position zero directly at the speaker sonar Parameters Seles statew Sonar carer frequency Hz 12000 air temperature C number of carriers The frame rate at which the phase is measured is 46 875 per second The phase must not change by more than z within one frame This limits the allowed speed of the microphone to about 8000 carrier frequency Example carrier 12000 Hz gt maxspeed 0 666 m s If this maximal velocity 1s exceeded the calibration of zero distance will be lost Be aware that 0 67 m s is a very slow
12. motion If you want to tolerate higher speeds the carrier frequency must be lower Multiple CW sonars can be used simultaneously by setting the number of carriers to values larger than 1 In this case the large pointer and the numerical display show the average distance determined from all carriers Additionally all individual distances are displayed by smaller colored pointers If these differ considerable the zero calibration obviously is lost at least for one of the carriers Distance Meter EB Distance Meter On the left side Distance Meter 2 2898 cm per rotation Distance Meter 10 cm per rotation 3 active a CW sonar actual position 4 7368 m actual position 1 5960 m with a single 3 carrier on the right side three carriers are used The Mathematics of the CW Sonar The Chirp The phase of a constant carrier is a linear function of time t p 0t The generated complex signal is given by x exp i The Transmitted and the Received Signal Only the real part of the generated signal x is sent The signal propagates through the air at the soundspeed c The propagation path may be s Then the signal is received after a pathdelay of At s c The imaginary part of the received signal is reconstructed from the received real part but with negative sign This complex signal is the complex conjugate of x t At y conj x t Ad The CW Sonar Algorithm z x y exp 1 o t exp o t At exp Ad
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