Measuring velocity of a target by Doppler shift, using improvements in calculating discrete Fourier transform

A method for determining the velocity of a target located in a medium, which method comprises the steps of:

• generating a transmitter electrical signal of prescribed frequency;
• transmitting into said medium coherent vibratory energy which is directed toward said target, said coherent vibratory energy being of a frequency in fixed relationship with said prescribed frequency, said transmitting being done in recurring transmission pulses of prescribed duration;
• receiving from said medium during intervals between said recurring transmission pulses said transmitted coherent vibratory energy after its interaction with said target;
• converting to a receiver electrical signal said received coherent vibratory energy;
• processing said receiver electrical signal to obtain a digital demodulated electrical signal indicative of the phase and frequency differences between said transmitter electrical signal and said receiver electrical signal;
• digitally filtering said digital demodulated electrical signal to separate it into complex digitized spectral components with a discrete Fourier transform procedure, said step of digitally filtering being repeated on a recursive basis and comprises the substeps of:
• latching each sample of said demodulated electrical signal for the period of k successive calculations during each of which calculations a respective one of k spectral components of the discrete Fourier transform of said demodulated electrical signal is calculated, said k spectral components having respective consecutive ordinal numbers selected from the consecutive ordinal numbers zeroeth through (N-1)th, N being a positive integer at least two;
• combining, with said latched sample of said demodulated electrical signal, a respective complex number during each of said k successive calculations, thereby to generate a correspondingly numbered one of said complex digital spectral components of the discrete Fourier transform;
• and
• multiplying said correspondingly numbered one of said complex digital spectral components by a fraction less than one of an Nth root of unity, to generate the next complex sample of said respective complex number;
• squaring an absolute value of each of the complex digitized spectral components to generate digital electric signals descriptive of the power spectrum of the interaction of said vibratory energy with said target;
• performing a comparative analysis of said digital electric signals descriptive of the power spectrum of the interaction of said vibratory energy with said target;
• and
• calculating the velocity of said target from the results of the comparative analysis of said digitized spectral components.

A method for determining the velocity of a target located in a medium, which method comprises the steps of:

• generating a transmitter electrical signal of prescribed frequency;
• transmitting into said medium coherent vibratory energy which is directed toward said target, said coherent vibratory energy being of a frequency in fixed relationship with said prescribed frequency, said transmitting being done in recurring transmission pulses of prescribed duration;
• receiving from said medium during intervals between said recurring transmission pulses said transmitted coherent vibratory energy after its interaction with said target;
• converting to a receiver electrical signal said received coherent vibratory energy;
• processing said receiver electrical signal to obtain a digital demodulated electrical signal indicative of the phase and frequency differences between said transmitter electrical signal and said receiver electrical signal;
• digitally filtering said digital demodulated electrical signal to separate it into a plurality k in number of complex digital spectral components in accordance with a discrete Fourier transform procedure, said k complex digital spectral components having respective consecutive ordinal numbers selected from the consecutive ordinal numbers zeroeth through (N-1)th, said step of digitally filtering comprises the substep of digitally filtering said digitized demodulated electrical signal on a recursive basis to convolve it with a window N samples wide, N being a positive integer at least two;
• and further comprises for each digital spectral component the respective substeps of:
• combining each sample of said demodulated electrical signal, as windowed by said rectangular window N samples wide, with a complex-number sample of a respective other signal identified by the same ordinal number as said digital spectral component being separated, thereby to generate each sample of said digital spectral component being separated;
• and
• multiplying said complex-number sample of said spectral component by a number substantially equal to an Nth root of unity to generate the next complex-number sample of said respective other signal identified by the same ordinal number as said digital spectral component being separated;
• squaring an absolute value of each complex sample of said complex digital spectral components to generate digital electric signals descriptive of the amplitudes of the power spectrum of the interaction of said vibratory energy with said target;
• performing a comparative analysis of said digital electric signals descriptive of the amplitudes of the power spectrum of the interaction of said vibratory energy with said target;
• and
• calculating the velocity of said target from the results of said comparative analysis.

A method for determining the velocity of a target located in a medium, which method comprises the steps of:

• generating a transmitter electrical signal of prescribed frequency;
• transmitting into said medium coherent vibratory energy which is directed toward said target, said coherent vibratory energy being of a frequency in fixed relationship with said prescribed frequency, said transmitting being done in recurring transmission pulses of prescribed duration;
• receiving from said medium during intervals between said recurring transmission pulses said transmitted coherent vibratory energy after its interaction with said target;
• converting to a receiver electrical signal said received coherent vibratory energy;
• processing said receiver electrical signal to obtain a digital demodulated electrical signal indicative of the phases and frequency differences between said transmitter electrical signal and said receiver electrical signal;
• digitally filtering said digital demodulated electrical signal to separate it into complex digitized spectral components with a discrete Fourier transform procedure, said step of digitally filtering comprises the substep of digitally filtering said digitized demodulated electrical signal on a recursive basis to convolve it with a window N samples wide, N being a positive integer at least two;
• and further comprises the substeps of:
• combining, with each sample of said demodulated electrical signal, as windowed by said rectangular window N samples wide, during each of which k calculations a respective one of k spectral components of the discrete Fourier transform of said demodulated electrical signal is calculated, said k spectral components having respective consecutive ordinal numbers selected from the consecutive ordinal numbers zeroeth through (N-1)th;
• combining, with said latched sample of said demodulated electrical signal, a respective complex number during each of said k successive calculations, said respective complex number identified by the same ordinal number as said successive calculation, thereby to generate a sample of the correspondingly numbered one of said separated complex digital spectral components;
• and
• respectively multiplying each of said complex digital spectral components by a respective Nth root of unity to generate the next complex-number sample of said respective other signal identified by the same ordinal number as said digital spectral component being separated;
• squaring an absolute value of each of the complex digitized spectral components to generate digital electric signals descriptive of the power spectrum of the interaction of said vibratory energy with said target;
• performing a comparative analysis of said digital electric signals descriptive of the power spectrum of the interaction of said vibratory energy with said target;
• and
• calculating the velocity of said target from the results of the comparative analysis of said digitized spectral components.

An apparatus for determining the velocity of a target located in a medium comprising:

• a) master clock for creating timing pulses;
• b) pulse repetition frequency generator (PRF) responsive to the master clock for creating a start pulse from the timing pulses;
• c) transmitter responsive to the PRF for transmitting pulses of coherent vibratory energy into said medium beginning when a start pulse is received;
• d) receiving transducer for receiving vibratory energy reflected from said target in said medium and creating an echo signal;
• f) time-gain control (TGC) generator coupled to the PRF for creating a gain control signal corresponding to a received start pulse;
• e) amplifier coupled to the receiving transducer and responsive to the TGC generator for amplifying the echo signal from the receiving transducer with a gain corresponding to the gain control signal;
• f) band pass filter coupled to the amplifier for filtering the amplified echo signal;
• g) phase shift unit for receiving the filtered amplified echo signal and creating a shifted signal;
• h) a range delay responsive to the PRF generator for creating a range gating signal corresponding to a received start pulse;
• i) first processing branch for receiving the filtered amplified echo signal and creating a real signal component r(t);
• j) second processing branch for receiving the shifted signal and creating an imaginary signal component i(t);
• k) recursive digital filter coupled to the first and second processing branches for creating a signal representing a complex digital Fourier transform (DFT) having a plurality of spectral components of the real signal component r(t) and imaginary signal component i(t) in real time;
• l) spectral component unit coupled to the recursive digital filter for creating a signal representing the amplitude of each spectral component;
• and
• m) velocity calculation means coupled to the spectral component unit for determining said velocity of said target in said medium from the signal representing the amplitude of each spectral component.