Zero State Machine

Mathematics, hacking and the daily struggle.

How to: Zero Delay State Variable Filter Part 4

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Nonlinear ZDF SVF part 2

Previously we derived a nonlinear zero delay feedback filter where the nonlinear tanh() elements were placed at the inputs of the integrators. This is not ideal, since it will lead to instabilities at high input amplitudes even with implicit integration.

Another way to model nonlinearities present in active analog integrators is to place the tanh() clipping at the “output” of the integrator, where it will limit the system to the $[-1, 1]$ interval.

ROPEmporium: Pivot 64-bit CTF Walkthrough With Radare2

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Preface

The challenge description together with the ELF binaries are located at https://ropemporium.com/challenge/pivot.html. The walkthrough will focus on Radare2 for the binary analysis and debugging, so basic knowledge is assumed. You should definitely learn how to use this free open source software!

In this post, the 64-bit binary will be cracked and analysed (see the 32-bit binary walkthrough here).

ROPEmporium: Pivot 32-bit CTF Walkthrough With Radare2

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Preface

The challenge together with the ELF binaries are located at https://ropemporium.com/challenge/pivot.html. This walkthrough will focus on using the Radare2 for the binary executable analysis and debugging, so basic knowledge of this awesome tool is assumed.

In this post, the 32-bit binary will be cracked and analysed and a future post will do the same for the 64-bit binary.

UPDATE: 64-bit walkthrough is here

How to: Zero Delay State Variable Filter Part 3

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Zero delay feedback SVF

We will now build a linear and nonlinear zero delay feedback filters starting from the state variable filter differential equation

How to: Zero Delay State Variable Filter Part 2

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In this part we will define what implicit integration is and develop the tools to solve differential equations with it.

Implicit vs. Explicit

Explicit integration of difference equations relies on information that is derived from the current and past steps. This seems like a very intuitive and natural idea - surely all dynamics we observe in our physical reality happen in this causal way. One thing follows from the past things - this is taken for granted by everyone.

How to: Zero Delay State Variable Filter Part 1

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Preface

According to traditional textbook DSP, digital IIR filter structures achieve phase shifting by using cascaded single sample delay blocks. This is in contrast to ‘real’ filters in the analog domain, where phase shifting is due electronical properties of capacitors and inductors - these electronic circuits contain no signal delaying elements and can be then called zero delay.

It then seems like achieving zero delay filtering in the digital domain is impossible, since we are stuck with delay elements by definition. This is not the case. To see how this is possible, we first have to understand what digital IIR filters are mathematically.