Pregunta
upstudy study bank question image url

Time left 1:29:18
Question 1
Not yet answered
Marked out of 8.00
P Flag question
Solve for the following signals
The FT of is:
Choose…
The FT of is:
Choose…
The FT of , where is the triangular function Choose…
The FT Of
Choose…
Question 2
Not yet answered
Marked out of 10.00
P Flag question
Consider the following signal:
The value of is
Choose…
The dc-value of the signal is Choose…
The average power is
The value of is
Choose…
The fundamental Frequency is
Choose…

Ask by Matthews Higgins. in Israel
Jan 30,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

Question 1:
  1. The Fourier Transform of is .
  2. The Fourier Transform of is .
  3. The Fourier Transform of is .
  4. The Fourier Transform of is .
Question 2:
  1. DC value = 2
  2. Average power = 10
  3. Fundamental frequency Hz

Solución

Let’s solve the problems step by step.

Question 1

  1. The FT of :
    The Fourier Transform (FT) of the sinc function is a rectangular function. The FT of is . Here, , so:
  2. The FT of :
    This is a linear function. The FT of is given by . Here, and :
  3. The FT of :
    The triangular function has a known FT. The FT of is . Here, :
  4. The FT of :
    The FT of is . The FT of is :

Question 2

  1. The value of :
    The Fourier series coefficient for can be calculated using the formula:
    Here, and . The average value of is , so:
  2. The dc-value of the signal :
    The DC value is the average value over one period:
    The average value of is and the average value of is :
  3. The average power:
    The average power can be calculated as:
    The average power of is and for is :
  4. The value of :
    The Fourier series coefficient can be calculated similarly. Since and functions do not contribute to negative frequencies, .
  5. The fundamental frequency :
    The fundamental frequency is given by:
    The period is the least common multiple of the periods of the components:

Summary of Answers

  1. FT of :
  2. FT of :
  3. FT of :
  4. FT of :
For Question 2:
  1. DC value = 2

Respondido por UpStudy AI y revisado por un tutor profesional

error msg
Explicar
Simplifique esta solución

Beyond the Answer

The Fourier Transform (FT) is a fascinating mathematical tool that transforms signals from the time domain into the frequency domain. It helps us analyze the frequencies contained in a signal, revealing critical insights about its behavior. For instance, the sinc function, prevalent in signal processing, has a rectangular shape in the frequency domain, demonstrating how the FT creates a correspondence between time and frequency!
Real-world applications of the Fourier Transform are everywhere! From audio signal processing, where it helps us manipulate sound waves for music production, to image compression techniques in JPEG files, FT enables efficient data handling. Even engineers use it to analyze vibrations in machinery. Understanding this transforms abstract math into a world of practical wonders!

Latest Other Questions

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad