Related Experiment Video
Updated: Jul 19, 2026
07:42
Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
Published on: December 15, 2021
Complex heterodyne for undersampled chirped sinusoidal signals
T M Niebauer1, A Schiel, D van Westrum
1Micro-g LaCoste Inc., Lafayette, CO 80026, USA. tim@crmr.net
Applied Optics
|October 28, 2006
Summary
A new complex heterodyne method analyzes frequency-chirped signals, enabling extraction below the Nyquist criterion. This reduces hardware costs for high-precision interferometer applications like gravity meters.
Area of Science:
- Signal Processing
- Physics
- Instrumentation
Background:
- Frequency-chirped sinusoidal signals are common in high-precision measurements.
- Traditional analysis methods require high sampling rates, increasing hardware costs.
- Interferometer applications often face challenges with differential acceleration.
Purpose of the Study:
- To introduce a novel method for analyzing frequency-chirped signals.
- To enable signal extraction below the Nyquist criterion.
- To reduce hardware requirements for data acquisition and signal processing.
Main Methods:
- Utilizing complex heterodyne analysis (complex demodulation) on digitized waveforms.
- Leveraging prior knowledge of the signal to reduce effective bandwidth.
- Applying the technique to high-precision interferometer data.
Main Results:
- Successful extraction of frequency-chirped signals sampled below the Nyquist rate.
- Demonstrated reduction in the effective bandwidth of the signal.
- Facilitation of less-expensive data acquisition and signal processing hardware.
Conclusions:
- The complex heterodyne method offers a cost-effective solution for analyzing frequency-chirped signals.
- This technique is particularly beneficial for high-precision applications like absolute gravity meters and gradiometers.
- The method allows for accurate signal recovery even with sub-Nyquist sampling.
Related Concept Videos
01:18Sinusoidal Sources
Direct current (DC) refers to an electric current that flows in a single direction, maintaining a constant polarity. This is in contrast to alternating current (AC), which periodically changes its direction and magnitude. AC forms the backbone of modern electricity transmission and distribution systems due to its efficient long-distance transmission capabilities.
In homes, the power supplies use sinusoidal sources to provide electricity. These sources generate a voltage that varies sinusoidally...
In homes, the power supplies use sinusoidal sources to provide electricity. These sources generate a voltage that varies sinusoidally...
01:18Aliasing
Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
01:22Upsampling
Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
01:11Sampling Continuous Time Signal
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
In the...
01:20Graphical and Analytic Representation of Sinusoids
Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
01:10Reconstruction of Signal using Interpolation
Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...