Ultrasonic Doppler Speedometer - Revision history

Yuzhen: /* Discussion and Improvement */

2025-04-29T04:24:28Z

Discussion and Improvement

← Older revision		Revision as of 12:24, 29 April 2025
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	==Discussion and Improvement==		==Discussion and Improvement==
	Current Applications:		===Current Applications===
	Ultrasonic Doppler speedometer technology has found broad applications across various industries due to its non-contact nature, high sensitivity, and robustness.：		Ultrasonic Doppler speedometer technology has found broad applications across various industries due to its non-contact nature, high sensitivity, and robustness.：

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	\|}		\|}

	Future Imrovement:		===Future Imrovement===

	Issues:		Issues:

Yuzhen: /* Discussion and Improvement */

2025-04-29T04:23:51Z

Discussion and Improvement

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 Future Imrovement:
-With the continued advancement of ultrasonic sensing and signal processing technologies, the future of ultrasonic Doppler speedometers is poised for significant growth. Miniaturization of transducer components, combined with the integration of machine learning and real-time data analytics, will dramatically enhance the system’s accuracy, adaptability, and range. Emerging applications are expected in autonomous vehicles for fine-grained environment sensing, in wearable medical devices for continuous health monitoring, and in smart infrastructure systems for structural health diagnostics. Research is also moving toward multi-modal sensing systems, where ultrasonic Doppler measurements are fused with optical, LiDAR, or radar data to enable highly resilient, precise tracking under diverse conditions. Improvements in materials science, such as the development of more efficient piezoelectric materials, will further extend the operational frequency range and sensitivity, pushing the frontiers of high-resolution, low-power motion detection
 ==References==

Yuzhen: /* Filtering and Signal Recovery */

2025-04-29T04:16:13Z

Filtering and Signal Recovery

← Older revision		Revision as of 12:16, 29 April 2025
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	The signal is now cleaner, and a clear frequency shift can be observed.		The signal is now cleaner, and a clear frequency shift can be observed.
	Taking the case of a receiver moving at 10 cm/s as an example, the mean frequency after filtering is approximately 40245.66 Hz, which is noticeably higher than the stationary case (≈40012.77 Hz). This shift is consistent with the expected Doppler effect caused by motion toward the source.		'''Taking the case of a receiver moving at 10 cm/s as an example, the mean frequency after filtering is approximately 40245.66 Hz, which is noticeably higher than the stationary case (≈40012.77 Hz). This shift is consistent with the expected Doppler effect caused by motion toward the source.'''

	[[File:DopplerFilteredSpectrum.png\|300px\|Filtered frequency spectrum with Doppler shift (mean frequency ≈ 40245.66 Hz)]]		[[File:DopplerFilteredSpectrum.png\|300px\|Filtered frequency spectrum with Doppler shift (mean frequency ≈ 40245.66 Hz)]]

Yuzhen: /* Reasults */

2025-04-29T04:15:03Z

Reasults

← Older revision		Revision as of 12:15, 29 April 2025
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	[[File:VelocityPlot.png\|300px\|Response time vs. distance]]		[[File:VelocityPlot.png\|300px\|Response time vs. distance]]

	In this plot, we can find the slope in the fitted curve around 338.95 m/s, which is close to the theoretical air sound velocity (343 m/s), with an error of around 1.18%.		'''In this plot, we can find the slope in the fitted curve around 338.95 m/s, which is close to the theoretical air sound velocity (343 m/s), with an error of around 1.18%.'''

	It is worth noting that the speed of sound in air is affected by several environmental factors:		It is worth noting that the speed of sound in air is affected by several environmental factors:

Yuzhen: /* Fast Fourier Transform (FFT) */

2025-04-29T04:09:00Z

Fast Fourier Transform (FFT)

← Older revision		Revision as of 12:09, 29 April 2025
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	The most widely used FFT algorithm is the Cooley-Tukey algorithm, which recursively breaks the DFT computation into smaller DFTs — especially effective when <math> N </math> is a power of two.		The most widely used FFT algorithm is the Cooley-Tukey algorithm, which recursively breaks the DFT computation into smaller DFTs — especially effective when <math> N </math> is a power of two.

	~~In this experiment, FFT is applied to both the transmitted and received signals to:~~

	~~Identify the dominant frequency, which corresponds to the ultrasound carrier (typically ~40 kHz),~~

	~~Design an appropriate band-pass filter centered around this frequency to eliminate noise,~~

	~~Visually inspect the spectrum for anomalies, harmonics, or interference.~~

	====Signal Filtering in the Frequency Domain====		====Signal Filtering in the Frequency Domain====

Yuzhen: /* Principles */

2025-04-29T04:07:03Z

Principles

← Older revision		Revision as of 12:07, 29 April 2025
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	Each <math> X_k </math> represents a specific frequency component of the signal. The magnitude <math> \|X_k\| </math> gives the amplitude of the corresponding frequency, and the argument <math> \arg(X_k) </math> provides its phase.		Each <math> X_k </math> represents a specific frequency component of the signal. The magnitude <math> \|X_k\| </math> gives the amplitude of the corresponding frequency, and the argument <math> \arg(X_k) </math> provides its phase.

	~~====Periodicity and Symmetry of the DFT====~~
	Because the DFT is based on a finite-length sequence, it implicitly assumes that the signal is periodic with period <math> N </math>. Moreover, for real-valued input signals (as is typical in this experiment), the DFT exhibits Hermitian symmetry:		Because the DFT is based on a finite-length sequence, it implicitly assumes that the signal is periodic with period <math> N </math>. Moreover, for real-valued input signals (as is typical in this experiment), the DFT exhibits Hermitian symmetry:

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	This property implies that only the first <math> N/2 </math> coefficients are needed to characterize the spectral content, since the second half is just the complex conjugate mirror image.		This property implies that only the first <math> N/2 </math> coefficients are needed to characterize the spectral content, since the second half is just the complex conjugate mirror image.

	~~====Frequency Resolution====~~
	The frequency corresponding to index <math> k </math> is:		The frequency corresponding to index <math> k </math> is:

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	The goodness of the linear fit validates the consistency of the signal processing pipeline and the physical model.		The goodness of the linear fit validates the consistency of the signal processing pipeline and the physical model.

	==Experiment==		==Experiment==

Yuzhen: /* Conclusion */

2025-04-29T04:01:27Z

Conclusion

← Older revision		Revision as of 12:01, 29 April 2025
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	The goodness of the linear fit validates the consistency of the signal processing pipeline and the physical model.		The goodness of the linear fit validates the consistency of the signal processing pipeline and the physical model.
	~~===Conclusion===~~
	This experiment demonstrates how ultrasonic distance estimation can be accurately implemented by combining time-domain thresholding and frequency-domain filtering. Proper filtering and frequency analysis are essential for reliable TOF detection in noisy environments.

	==Experiment==		==Experiment==

Yuzhen: /* Frequency Analysis */

2025-04-29T04:01:08Z

Frequency Analysis

← Older revision		Revision as of 12:01, 29 April 2025
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	<math> x_n^{\mathrm{filtered}} = \frac{1}{N} \sum_{k=0}^{N-1} X_k^{\mathrm{filtered}} \cdot e^{2\pi i kn/N} </math>		<math> x_n^{\mathrm{filtered}} = \frac{1}{N} \sum_{k=0}^{N-1} X_k^{\mathrm{filtered}} \cdot e^{2\pi i kn/N} </math>
	This process removes irrelevant frequencies and enhances the signal-to-noise ratio, enabling more reliable detection of the echo pulse.		This process removes irrelevant frequencies and enhances the signal-to-noise ratio, enabling more reliable detection of the echo pulse.


	===Time Thresholding and TOF Detection===		===Time Thresholding and TOF Detection===

Yuzhen: /* Magnitude Spectrum and Spectral Peaks */

2025-04-29T03:59:01Z

Magnitude Spectrum and Spectral Peaks

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	Visually inspect the spectrum for anomalies, harmonics, or interference.		Visually inspect the spectrum for anomalies, harmonics, or interference.

	~~====Magnitude Spectrum and Spectral Peaks====~~
	~~The magnitude spectrum is computed as:~~

	~~<math> \|X_k\| = \sqrt{ \text{Re}(X_k)^2 + \text{Im}(X_k)^2 } </math>~~
	By plotting <math> \|X_k\| </math> versus <math> f_k </math>, the dominant frequency can be observed as the frequency with the highest amplitude peak. This forms the basis of frequency-domain filtering strategies used later in the experiment.

	====Signal Filtering in the Frequency Domain====		====Signal Filtering in the Frequency Domain====

Yuzhen at 03:58, 29 April 2025

2025-04-29T03:58:13Z

← Older revision		Revision as of 11:58, 29 April 2025
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	This method assumes straight-line propagation, negligible reflection loss, and consistent environmental conditions.		This method assumes straight-line propagation, negligible reflection loss, and consistent environmental conditions.

	===Frequency Analysis: Discrete Fourier Transform===		===Frequency Analysis===

			====Discrete Fourier Transform====

	In order to analyze the spectral content of a time-domain signal — especially to extract the dominant frequency component of the ultrasound wave — the Discrete Fourier Transform (DFT) is employed. The DFT is a powerful tool that transforms a sequence of time-domain samples into a set of complex frequency components.		In order to analyze the spectral content of a time-domain signal — especially to extract the dominant frequency component of the ultrasound wave — the Discrete Fourier Transform (DFT) is employed. The DFT is a powerful tool that transforms a sequence of time-domain samples into a set of complex frequency components.

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	By plotting <math> \|X_k\| </math> versus <math> f_k </math>, the dominant frequency can be observed as the frequency with the highest amplitude peak. This forms the basis of frequency-domain filtering strategies used later in the experiment.		By plotting <math> \|X_k\| </math> versus <math> f_k </math>, the dominant frequency can be observed as the frequency with the highest amplitude peak. This forms the basis of frequency-domain filtering strategies used later in the experiment.

	===Signal Filtering in the Frequency Domain===		====Signal Filtering in the Frequency Domain====
	In practice, ultrasonic signals are contaminated with environmental noise and harmonics. To isolate the desired frequency band around the central ultrasonic frequency (e.g., 40 kHz), a band-pass filter is designed in the frequency domain.		In practice, ultrasonic signals are contaminated with environmental noise and harmonics. To isolate the desired frequency band around the central ultrasonic frequency (e.g., 40 kHz), a band-pass filter is designed in the frequency domain.