Related Experiment Video
Updated: May 10, 2025
07:42
Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
Published on: December 15, 2021
3.0K
Taylor Series Interpolation-Based Direct Digital Frequency Synthesizer with High Memory Compression Ratio.
Kalle I Palomäki1, Jari Nurmi1
1Wireless Research Center, Tampere University, 33720 Tampere, Finland.
Sensors (Basel, Switzerland)
|April 26, 2025
Summary
This study introduces a novel 16-bit quadrature direct digital frequency synthesizer (DDFS) achieving high memory compression (5178:1) and excellent signal purity (-102.9 dBc SFDR) using Taylor series interpolation.
Area of Science:
- Digital Signal Processing
- Integrated Circuit Design
Background:
- Direct digital frequency synthesizers (DDFSs) face challenges in balancing memory compression with output signal purity.
- Efficient phase-to-amplitude conversion is crucial for DDFS performance.
Purpose of the Study:
- To present a 16-bit quadrature DDFS design that enhances memory compression and signal purity.
- To demonstrate the effectiveness of second-order Taylor series polynomial interpolation for phase-to-amplitude conversion in DDFS.
Main Methods:
- Utilized second-order Taylor series polynomial interpolation for phase-to-amplitude conversion.
- Implemented a segmented look-up table (LUT) approach optimized with a Python model.
- Designed and synthesized the DDFS using register-transfer level VHDL and implemented on an AMD Artix 7 FPGA.
Main Results:
- Achieved a memory compression ratio of 5178:1.
- Generated sine and cosine outputs with high spectral purity, reaching a spurious-free dynamic range (SFDR) of -102.9 dBc.
- Required minimal FPGA resources: 107 logic slices and 3 DSP slices.
Conclusions:
- The proposed DDFS design effectively overcomes the trade-off between memory compression and signal purity.
- Second-order Taylor series interpolation offers a resource-efficient method for high-performance DDFS.
- The design demonstrates practical feasibility through FPGA implementation with competitive resource utilization.
Related Concept Videos
01:10Reconstruction of Signal using Interpolation
145
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...
145
01:20Discrete-Time Fourier Series
183
The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
For a discrete-time periodic signal x[n]...
183
01:26Linear Approximation in Frequency Domain
79
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
79
01:26Discrete-time Fourier transform
222
The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
One of the notable...
222
01:20Downsampling
109
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
109
01:22Upsampling
161
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...
161