Step 1: Define the signal parameters.Original signal frequency: \( f_{in} = 1 \text{ kHz} = 1000 \text{ Hz} \).Sampling frequency: \( f_s = 1800 \text{ samples/sec} = 1800 \text{ Hz} \).
Step 2: Assess aliasing potential.The Nyquist rate for perfect signal reconstruction is \( 2f_{in} = 2 \times 1000 = 2000 \text{ Hz} \).The Nyquist frequency, determined by the sampling process, is \( f_s/2 = 1800/2 = 900 \text{ Hz} \).Aliasing will occur because the sampling frequency \( f_s = 1800 \text{ Hz} \) is below the Nyquist rate of 2000 Hz (or, equivalently, \(f_{in}>f_s/2\)).
Step 3: Identify frequencies after sampling.Sampling a signal with frequency \(f_{in}\) at \(f_s\) results in spectral components at frequencies \( |f_{in} \pm k f_s| \) for all integers \(k\).Focus is on frequencies in the low-frequency range.For k=0: \( f = f_{in} = 1000 \text{ Hz} \).For k=1: \( f = |f_{in} - f_s| = |1000 - 1800| = 800 \text{ Hz} \). Additionally, \(f_{in}+f_s = 2800\) Hz, and so on.Therefore, the baseband contains components at 1000 Hz and an aliased component at 800 Hz after sampling.
Step 4: Apply the low-pass filter.The signal passes through an ideal low-pass filter with \( f_{cutoff} = 1100 \text{ Hz} \).This filter passes frequencies below 1100 Hz and blocks higher frequencies.The signal contains frequencies at 800 Hz, 1000 Hz, 2800 Hz, etc.The filter transmits the 800 Hz and 1000 Hz components since both are below 1100 Hz.The filter output includes both the 800 Hz and 1000 Hz frequency components.