Wavelet Transform

This repo has rtl and scripts for wavelet transform targeting a stream of 8-bit inputs for submission with the MPW6 shuttle as part of the Zero to ASIC Course.

A wavelet transform is like a fourier transform, but has some very advantageous properties ([see this readme section for more details](#Some Interesting Properties)).

For usage details about the transform see the following sections.

Usage: Clocking in Input Bytes and Reading Output Byes

Clocking in Input Bytes

1. Set up 8-bits on 8 gpios (the i_value inputs).
2. "clock-in" these values by creating a rising edge of the i_data_clk signal.

NOTE: all filters complete the computation after one clock cycle.

Reading out Output Bytes

1. Set o_select_output_channel gpios to desired filter for readout
2. Wait a couple cycles (crossing clock domains)
3. Read the 8-bits (in parallel) from o_multiplexed_wavelet_out

Process for scaling up the transform

Scaling up to cover a larger range of input frequencies involves:

1. In wavelet_transform.v: add new fir module with the parameters from WT.py (see next section)
2. In wavelet_transform.v: incrementing TOTAL_FILTERS parameter
3. In wavelet_transform.v: update the TOTAL_TAPS parameter (# bits in largest filter)

Generating parameters from WT.py

To help with the math of scaling up the transform, use the following python script located at the follwing path:

.
└── wavelet_transform
    └── py
        └── WT.py

Change the parameters for generating the new Wavelet_Array object.

For example increasing from the default 8 filters to 16:

wa = Wavelet_Array(base_num_elem=3, max_wavelet_order=16)

Next, print the filter element values in either decimal or hex (two's complement) representation:

wa.print_all_filters() # decimal representation
wa.print_all_filters_hex() # hex representation

Some Interesting Wavelet Properties

The 1-D wavelet transform can be seen as an alternative to the FT transform on time-series data.

Essentially it's a convolution of a small wave or 'wavelet'.

Typically, the shape of the wavelet is the same for each of ranges of interest, just scaled, making construction of the transform two steps:

1. Base wavelet equation (this repo uses the Ricker Wavelet family of wavelets)
2. Scaling of the wavelet to larger size (smaller frequencies)

Wavelets Retain Phase Data

With wavelet's one sees not just the intensity of frequency, but whether high or low at that point in time.

This is very interesting to monitoring and especially extrapolating patterns in data.

Wavelets Increase Temporal Resolution (when compared to Fourier Transform)

Unlike the fft (which uses same time scale for multiple frequencies), each frequency range has very high temporal localization.

This also means different resolution between different frequencies, higher frequencies will have higher temporal resolution.

Will be better or at par with temporal resolution than the fourier frequency transform.

Zero to ASIC Course

This project was made as part of the Zero to ASIC Course!

License

This project is licensed under Apache 2