Streaming DFT for Radar Sensors With Low Memory Footprint
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Solution Overview
Problem
Existing sensor devices, such as RADAR devices, face high memory consumption due to the need to store all signal samples before performing a Fourier spectral analysis, making it expensive to embed DFT in computing platforms with limited hardware resources.
Innovation Solution
A method for applying a P-dimensional Discrete Fourier Transform (DFT) to a sequence of sensor samples, where each sample's spectral contribution is computed iteratively and stored only temporarily, reducing the need for large memory by processing samples one at a time or in groups, and using a processor circuit to generate DFT vectors based on order indices and phasor values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all N signal samples are acquired and stored in advance to perform FFT spectral transform, then the spectral analysis can be performed with high resolution, but the memory consumption becomes very high
Solution Approach 1:
The patent segments the DFT computation into N individual steps, where each step processes one sample xn and computes its spectral contribution Δy(n) separately. This segmentation allows the system to process samples sequentially rather than requiring all samples to be stored simultaneously, reducing memory consumption from O(N) to O(1) for sample storage while maintaining full spectral resolution through the accumulation of all N spectral contributions.
Solution Approach 2:
The patent pre-computes and stores the DFT vectors d(n) = [exp(-i2πf1t1), exp(-i2πf2t1), ..., exp(-i2πfPt1)] for each sample position n before actual signal processing. These pre-computed complex exponential factors are reused for each sample, eliminating the need to recalculate them and reducing the computational burden during real-time processing while maintaining spectral accuracy.
2Reliability
If bigger memory modules are needed to store all signal samples, then the DFT can be performed accurately, but the cost of embedding the transform in a computing platform becomes expensive
Solution Approach 1:
The patent divides the DFT computation into N sequential operations, each handling one sample. This segmentation eliminates the need for large memory modules to store all N samples simultaneously, reducing hardware costs while maintaining computational accuracy through the accumulation formula y(N) = Σ(n=1 to N) Δy(n), where each Δy(n) = d(n)·xn is computed and added to the running total.
Solution Approach 2:
The patent extracts only the essential computational elements needed for DFT - the complex exponential factors and the accumulation mechanism - and removes the requirement for large sample storage memory. By taking out the sample storage requirement and replacing it with sequential processing and accumulation, the system achieves accurate DFT computation with minimal memory resources, reducing embedding costs.
3Quantity of substance
If signal samples are processed one at a time with iterative spectral contribution computation, then memory footprint is reduced, but the computational complexity increases
Solution Approach 1:
The patent segments the DFT computation into N simple iterative steps, where each step involves only one multiplication (Δy(n) = d(n)·xn) and one vector addition (y(n) = Δy(n) + y(n-1)). This segmentation reduces memory footprint to O(1) for sample storage while distributing the computational load evenly across N simple operations, making the overall complexity manageable through parallelization or sequential processing.
Solution Approach 2:
The patent changes the computational approach from batch processing (computing DFT on all N samples simultaneously requiring O(N) memory) to iterative processing (computing spectral contribution of each sample sequentially with O(1) memory). This parameter change in processing mode transforms the memory-complexity tradeoff, reducing memory footprint while maintaining computational feasibility through the use of pre-computed DFT vectors and simple accumulation operations.
Data Source
AI summary
A method for applying a Discrete Fourier Transform (“DFT”) to a sequence of N samples of a sensor signal, with N>2. The resulting DFT spectral coefficients are updated iteratively whenever a new one of the samples or a sub-group of consecutive new samples, comprising a predefined number J of samples, with 1<J<N, is received.