Up_and_R

 I'm up and running on IBM's Qiskit, thanks to this step-by-step

set-up video. Change the 1s and -1s as I please, the result is always .25

probability at each of the States.  

Followed the instructiond to the letter, except my Python version is 1.10.9

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The Fourier Checking algorithm is a quantum algorithm used in the context of promise problems. Let’s break it down:

1. Promise Problems:

   • Promise problems are a type of decision problem where the input is a promise that the solution satisfies certain properties.
   • In the case of Fourier Checking, we have two functions: f and g.

2. Fourier Checking Problem:

   • The Fourier Checking problem aims to decide if function f is correlated with the Fourier transform of function g.
   • The Fourier transform of a function is a mathematical operation that reveals its frequency components.
   • In this context, we’re interested in whether f and the Fourier transform of g exhibit any correlation.

From Simple English Wikipedia, the free encyclopedia

The Fourier transform is a mathematical function that can be used to find the base frequencies that a wave is made of. Imagine playing a chord on a piano. When played, the sounds of the notes of the chord mix together and form a sound wave. This works because each of the different note's waves interfere with each other by adding together or canceling out at different points in the wave. A Fourier transform takes this complex wave and is able to find the frequencies that made it, meaning it can find the notes that a chord is made from.

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Asked Bing/Chat about adjusting the bass and treble on a song...

You

But I need a Fourier transform to separate the different frequencies to begin with...

Copilot

You’re absolutely right! My apologies for the oversight. To separate different frequencies in a signal, you indeed need the Fourier Transform. Let’s delve into this further:

Frequency Separation with Fourier Transform:

The Fourier Transform is a powerful tool that allows you to analyze a signal in terms of its frequency components.

By applying the Fourier Transform, you can break down a complex signal into its constituent sinusoidal components at different frequencies.

This separation enables you to understand which frequencies contribute to the overall signal.

Steps to Separate Frequencies:

Given a signal (such as an audio waveform), follow these steps:

Apply the Fourier Transform: Convert the signal from the time domain to the frequency domain using the Fourier Transform.

Observe the Spectrum: The resulting frequency spectrum will show the amplitudes and phases of different frequency components.

Filtering: To separate specific frequencies, you can apply filters:

Low-Pass Filter: Allows only low-frequency components (e.g., bass) to pass through.

High-Pass Filter: Allows only high-frequency components (e.g., treble) to pass through.

Band-Pass Filter: Selects a specific range of frequencies.

Inverse Fourier Transform: If needed, you can convert the filtered spectrum back to the time domain using the inverse Fourier Transform.

Real-World Examples:

Audio Equalization: Adjusting treble and bass in music involves modifying specific frequency bands using filters.

Speech Recognition: Separating speech features (such as formants) relies on frequency analysis.

Image Processing: Fourier Transform helps remove periodic noise patterns (e.g., moiré patterns) from images.

Remember that the Fourier Transform is your go-to tool for understanding and manipulating frequency content in signals. Thanks for pointing that out, and happy signal processing! 🎵🔊📈