Question E7F01:
What is meant by “direct sampling” in software defined radios?  

Choices:  
A: Software is converted from source code to object code during operation of the receiver  
B: I and Q signals are generated by digital processing without the use of RF amplification  
C: Incoming RF is digitized by an analog-to-digital converter without being mixed with a local oscillator signal  
D: A switching mixer is used to generate I and Q signals directly from the RF input    

Correct Answer is  C: Incoming RF is digitized by an analog-to-digital converter without being mixed with a local oscillator signal  

Correct Answer: C — Incoming RF is digitized by an analog-to-digital converter without being mixed with a local oscillator signal.

1) Why C is correct
- “Direct sampling” means the ADC takes samples of the RF signal directly at its RF frequency. There is no analog frequency conversion (no LO, no analog mixer) before the ADC. After digitizing, digital downconversion (DDC) creates I/Q in DSP.

2) Why the other choices are incorrect
- A: Describes how software is compiled (source to object code). That has nothing to do with RF signal paths or SDR architectures.
- B: Claims I and Q are generated by digital processing “without the use of RF amplification.” Direct sampling does not preclude RF amplification (LNAs are commonly used). The key is “no analog mixing,” not “no amplification.”
- D: A switching mixer producing I/Q from RF is a direct-conversion (zero-IF) receiver. It still uses a local oscillator and analog mixing, so it’s not direct sampling.

3) Useful formulas and rules of thumb
- Nyquist for baseband:
  $$f_s \ge 2B$$
  where $B$ is the signal bandwidth.
- Bandpass (RF) sampling: you can sample an RF band directly if you meet both:
  - $$f_s \ge 2B$$
  - Choose $f_s$ so the desired RF band aliases to a unique, non-overlapping band at baseband or low IF:
    $$f_{alias} = |f_{RF} - N f_s|$$
    for some integer $N$, with appropriate preselection filtering to avoid out-of-band aliases.
- ADC dynamic range (rule of thumb):
  $$SNR_{ADC} \approx 6.02N + 1.76 \text{ dB}$$
  where $N$ is ADC resolution in bits.
- Practical notes:
  - Direct sampling needs a high-speed, high-dynamic-range ADC plus strong RF preselection (band-pass filter) and usually an LNA.
  - I/Q is typically produced after the ADC by multiplying with a digital NCO and low-pass filtering (DDC).