Sheet 3 Fourier Series and Signal Analysis PDF

Sheet 3 1. Find the Exponential Fourier series of the periodic signal 𝑔𝑃 (t), sketch the Fourier coefficient spectrum at  𝑇𝑜 =2𝜏.  𝑇𝑜 =5𝜏. ∞ 𝑡 − 𝑛𝑇𝑜 𝑔𝑃 (t) = ∑ 𝐴 𝒓𝒆𝒄𝒕 ( )...

Sheet 3 1. Find the Exponential Fourier series of the periodic signal 𝑔𝑃 (t), sketch the Fourier coefficient spectrum at  𝑇𝑜 =2𝜏.  𝑇𝑜 =5𝜏. ∞ 𝑡 − 𝑛𝑇𝑜 𝑔𝑃 (t) = ∑ 𝐴 𝒓𝒆𝒄𝒕 ( ) 𝜏 𝑛=−∞ 2. Find the Exponential Fourier series for 𝑔𝑃 (t), sketch the Fourier coefficient spectrum at 𝑇𝑜 =2𝜏. ∞ 𝑡 − 𝑛𝑇𝑜 𝑔𝑃 (t) = ∑ 𝐴 Ʌ ( ) 𝜏 𝑛=−∞ 3. You have the following signal ∞ 𝑔𝑃 (t) = 4 ∑ 𝒕𝒓𝒊 (𝟐 × 10−3 𝑡 − 4n) 𝑛=−∞  sketch this signal 𝑔𝑃 (t) in time domain   Find the Fourier series and sketch the Fourier coefficient spectrum.  Find the power contents in each of the following frequency components (0 HZ, 4 KHZ, 8 KHZ, and 12 KHZ). 4. You have the following signal ∞ 𝑔𝑃 (t) = ∑ 8 𝒓𝒆𝒄𝒕 (104 − 5n) 𝑛=−∞  sketch this signal 𝑔𝑃 (t) in time domain  Find the Fourier series and sketch the Fourier series coefficient 𝐶𝑛.  Find and sketch 𝑔𝑃 (t) , S(f).  Calculate the power of components at (0 HZ, 1 KHZ, and 2 KHZ).  If 𝑔𝑃 (t) is applied to a Band path filter (B.P.F) centered at 2 KHZ and band width B.W= 1 KHZ , sketch its output in time and frequency domain.