A Colorful Introduction to Complex Numbers and Fourier Analysis
Complex numbers is the math of oscillators: processes that repeat themselves. The original term was Sanskrit ?jya? meaning “bowstring.” That's a nice.
Fourier Transforms and the Fast Fourier Transform (FFT) Algorithm
Definition of the Fourier Transform shorthand: X ? Y. If z is a complex number and z = x + iy where x and y are its real and imaginary parts then the ...
The Scientist and Engineers Guide to Digital Signal Processing The
Although complex numbers are fundamentally disconnected from our reality In Chapter 8 we defined the real version of the Discrete Fourier Transform.
UFMC Transceiver Complexity Reduction
10 juil. 2018 the FFT size the number of complex multipliers and adders can be reduced. ... complexity of the output pruning
Fourier Transforms DFTs
https://www.me.psu.edu/cimbala/me345web_Fall_2014/Lectures/Fourier_Transforms_DFTs_FFTs.pdf
FFT-Based Algorithm for Metering Applications
The DFT of a finite-length sequence of size N is defined as follows: The FFT implementation in power meters requires complex number computing ...
Introduction to the DSP Subsystem in the IWR6843
Counting the number of detected objects in a given volume windowing FFT
Error analysis of some operations involved in the Cooley-Tukey Fast
FFT of a vector assuming that all terms of have real and imaginary error that can occur when multiplying a complex number by a root of unity in.
C8051F12X FAMILY Relevant Devices Introduction Radix-2 FFT
(A' and B') of the butterfly are complex numbers containing the data that is 5) The algorithm is a Radix-2 type meaning that the number of samples must.
The Fundamentals of FFT-Based Signal Analysis and Measurement
is the root mean square (rms) amplitude of the sinusoidal component at frequency k. Thus the units of a power spectrum are often referred to as quantity
ADC Buffer
(32 KB)ADC Buffer (32 KB) EDMA engine L3 (1MB)Handshake RAM
(32 KB)Primarily for storing
the radar-cubeFor sharing data (e.g.
detected objects) betweenDSP and R4F (MSS).
Signal processing on the ADC
data (interference mitigation), advanced detection algorithms, highter layer algorithmsADC data from the
digital front-endRange, Doppler, Azimuth
FFTs, Detection (CFAR-CA)Efficient transfer of data between memories (ADC Buffer, L2, L3, HWAMEM, Handshake RAM)
L2 program/data128 KB
L2 program/data128 KB
L31024 KB
L1P32 KB256 bits
64 bits
L1D32 KB64 bits256 bits256 bits
L1 runs at CPUT clock (600 MHz)
L2 runs at CPU/2 (300 MHz)
L3 runs at CPU/3 (200 MHz)
Input Formatter Output Formatter
CoreComputational
Unit Input samples
(24-bit I, 24-bit Q)From Accelerator
local memoryTo Accelerator local memoryACCELERATOR ENGINE
State Machine512-byte RAM
Trigger to DMA/Processor
Trigger from DMA/
Processor/Ping-Pong bufferOutput samples
(24-bit I, 24-bit Q)Static (common)
registersACCEL_MEM0
(16 KB)ACCEL_MEM1 (16 KB)ACCEL_MEM2 (16 KB)ACCEL_MEM3 (16 KB)Accelerator Local Memories128-bit wide bus interconnect
From/To
DMA/Processor
Parameter-Set
Config Memory
ADCBufferInterference
Mitigation
(DSP L1)Range FFT (16 bit) L3Doppler
FFT (16 bit) L3 NonCoherent
Summation
L3/L2DetectionAngle-
FFTTracking/
ClusteringHandshake
Memory
radar-cuberadar-cube antennasantennas range range chirpschirpsPre-Detection
Matrix
range dopplerLEGEND
HWADSP/HWA
DSP ADCBufferInterference
Mitigation
(DSP L1)Range FFT (16 bit) L3Doppler
FFT (24 bit)L3/L2DetectionAngle-
FFTTracking/
ClusteringHandshake
Memory
radar-cube antennas range chirpsPre-Detection
Matrix
range dopplerLEGEND
HWADSP/HWA
DSP NonCoherent
Summation
DSP_fft16x3224136981614883503683116078
DSP_fft32x3226141395617724267836319914
DSPF_sp_fftS
PxSP305473106619624683916321740
Range bins
L3 Memory
Chirp 1
Chirp 2
Chirp N
DSP/HWA Memory
" Transpoose read speeds : 1 cycle (@200Mhz) per sample " One line of 256 samples takes 1.28 μs to be transferred from DSP memory to L3 After processing128 chirps
256 x 4 rows
128 chirps
L3 Memory
Range FFT channel #1Range FFT channel #2Range FFT channel #3Range FF4T channel #2L3 Memory
Transpose write speeds : 4
Cycles (@200MHz) per sample
-4 channel x 256Samples/channels takes 21 us
To be transferred to L3
Data is contiguously placed
to Make subsequent transfer to DSP/HWA (for doppler processsing) fast.256 samples
Text Here
Ant 1 Ant 4 Ant 3 Ant 5HWA Processing:
FFT + windowing
Processing time is 6.5 μs for 4 Rx channelsATranspose transfer to L3Will take 21 μs using 1 DMA
L3 Memory
BText Here
Ant 1 Ant 4 Ant 3 Ant 5256 samples
Text Here
Range FFT channel #1
Range FFT channel #2
Range FFT channel #3
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