Optimized Design of Direct Digital Frequency Synthesizer Based on Hermite Interpolation
Kunpeng Zhou1, Qiaoyu Xu1, Tianle Zhang1
1College of Mechanical and Electrical Engineering, Henan University of Science and Technology, Luoyang 471000, China.
Sensors (Basel, Switzerland)
|October 16, 2024
Summary
This study introduces an optimized Direct Digital Frequency Synthesis (DDFS) method using cubic Hermite interpolation to improve spectral purity and reduce resource usage in embedded systems.
Area of Science:
- Digital Signal Processing
- Embedded Systems Engineering
Background:
- Direct Digital Frequency Synthesis (DDFS) often suffers from suboptimal spectral purity in resource-constrained environments.
- Amplitude quantization during DDFS digitalization introduces spurious issues and requires significant data storage.
Purpose of the Study:
- To propose an optimized DDFS technique using cubic Hermite interpolation.
- To enhance spectral purity and reduce resource utilization in DDFS for embedded systems.
Main Methods:
- Implemented DDFS hardware architecture on a Field-Programmable Gate Array (FPGA).
- Extracted interpolation parameters using cubic Hermite interpolation, combining derivative relations of sine/cosine functions with dual-port ROM.
- Employed single-quadrant ROM compression technology to minimize storage space.
Main Results:
- Achieved a ROM resource compression ratio of 1792:1.
- Obtained a 14-bit output Spurious-Free Dynamic Range (SFDR) of -88.134 dBc.
- Significantly improved amplitude quantization precision and reduced spurious levels.
Conclusions:
- The proposed optimized DDFS scheme enhances spectral performance and resource efficiency.
- This technique is highly suitable for resource-constrained embedded systems, radar, and communication systems.
Related Concept Videos
Reconstruction of Signal using Interpolation
178
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...
178
Linear Approximation in Frequency Domain
87
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....
87
Discrete-time Fourier transform
278
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...
278
Linear Approximation in Time Domain
68
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
68
Basic Discrete Time Signals
200
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
200
Design Example: Underdamped Parallel RLC Circuit
270
Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...
Starting with a fixed...
270


