https://file.aiquickdraw.com/mathbot/file/1724693332647wdd7xcdp.jpg

c'est un tp a faire sur octave ou mathlab

I can help you with the assignment. Let me first transcribe the content from the image and provide an analysis of the task.

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### Image Transcription:

**Titre : Traitement Numérique d'Images - Session Pratique**

**Exercice 1 (10 points) :**
Soit la fonction \( f(x) = \sin(2\pi x) + \frac{1}{2}\cos(4\pi x) \).

#### Étapes pour réaliser cet exercice :

1. **Définir cette fonction dans une fonction MATLAB ou Octave.**
2. **Tracer cette fonction pour la plage \( x \in [0, 1] \) avec un pas de 0.01.**
3. **Ajouter du bruit gaussien à cette fonction, puis tracer à nouveau la fonction bruitée.**
4. **Utiliser une méthode de filtrage pour réduire le bruit. Comparer la fonction filtrée avec la fonction initiale.**
5. **Calculer et tracer l'erreur quadratique entre la fonction initiale et la fonction filtrée.**
6. **Utiliser un outil de débruitage basé sur les ondelettes, puis comparer la fonction débruitée avec la fonction initiale et la fonction bruitée.**

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### Analysis and Next Steps:

This assignment involves several tasks that require the use of MATLAB or Octave to work with a specific mathematical function, apply noise, and filter it. Here's a breakdown of what you need to do:

1. **Define the Function:** 
   You'll start by writing a MATLAB or Octave function that defines \( f(x) = \sin(2\pi x) + \frac{1}{2}\cos(4\pi x) \).

2. **Plot the Function:**
   Plot the function over the interval \([0, 1]\) with a step size of 0.01.

3. **Add Gaussian Noise:**
   Introduce Gaussian noise to the function and plot the noisy version.

4. **Filter the Noise:**
   Apply a filtering method (e.g., a low-pass filter) to reduce the noise and compare the filtered function with the original.

5. **Calculate the Quadratic Error:**
   Calculate and plot the quadratic error between the original and the filtered functions.

6. **Denoising with Wavelets:**
   Use a wavelet-based denoising technique and compare the denoised function with both the original and noisy functions.

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### Do you need detailed guidance on any specific step? Let me know if you have any questions or need further explanations on any of these tasks.

Here are some questions that might be useful for you to consider:
1. What is the purpose of adding Gaussian noise to the function?
2. How does filtering affect the signal, and why is it important?
3. What are the advantages of using wavelet-based denoising compared to simple filtering?
4. How is the quadratic error calculated, and why is it a useful measure?
5. What are the key differences between MATLAB and Octave for this kind of task?

**Tip:** When working with noise and filtering, always check how the noise affects different parts of the signal, and whether your filter preserves the important features of the signal while reducing the noise.

Explore a MATLAB/Octave assignment on digital signal processing involving the addition of Gaussian noise, filtering techniques, and wavelet denoising. Understand the impact of noise on signals and the effectiveness of various denoising methods.

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