--- title: "Speech characteristics and linear predictive coder" subject: "Wireless Communication" chapter: 6 key: "semester_7/wireless_communication:speech-lpc" source: https://www.bctengineer.com/q/semester_7/wireless_communication/speech-lpc site: BCT Engineering --- # Speech characteristics and linear predictive coder Wireless Communication · Chapter 6: Speech and Channel Coding - Asked in: 2080 Baisakh, 2+6 marks; 2079 Bhadra, 3+5 marks; 2076 Bhadra, 3+5 marks; 2075 Bhadra, 2+6 marks; 2072 Magh, 2+6 marks (asked 5 times) - Video: [Characteristics of speech signals Chapter-6 part-1](https://www.youtube.com/watch?v=t5_394QJE9g) — IOE Electronics and communication engineering - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/speech-lpc - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-6 ## Question What are the characteristics of speech signal? Explain the operation of linear predictive coder (LPC) with neat block diagram. ## Short answer Speech is band-limited (300-3400 Hz), quasi-stationary over 20 ms frames, with voiced/unvoiced excitation, pitch periodicity, and high sample correlation. LPC models the vocal tract as an all-pole filter, predicting each sample from previous ones using coefficients a_k; encoder transmits coefficients, gain, pitch, and voiced/unvoiced flag; decoder excites a synthesis filter with pulse trains or noise to reconstruct speech. ## Answer #### Characteristics of speech signal - **Bandwidth:** most energy and intelligibility lie in about 300–3400 Hz (telephone band). - **Non-uniform amplitude distribution:** small amplitudes are much more likely than large ones (Laplacian-like pdf), so non-uniform quantization helps. - **Short-term stationarity:** speech is quasi-stationary over 10–30 ms, so it can be analysed in frames. - **Voiced and unvoiced sounds:** voiced sounds (vowels) are quasi-periodic with a **pitch** of roughly 80–350 Hz; unvoiced sounds (s, f, sh) are noise-like. - **Formants:** the vocal tract resonances give spectral peaks (formants) that carry most information. - **High correlation** between adjacent samples and pitch periods, so speech is predictable. - **Silence:** about 40–60% of a conversation is pauses, used by voice activity detection. - **Non-flat spectrum:** energy falls at higher frequencies. #### Linear predictive coder (LPC) **LPC** is a vocoder that models the vocal tract as an all-pole digital filter and sends only the filter parameters plus the excitation type, instead of the waveform. Each sample is predicted as a linear combination of the previous *p* samples: ŝ(n) = Σₖ₌₁ᵖ aₖ · s(n − k) The coefficients aₖ are chosen to minimise the mean square prediction error e(n) = s(n) − ŝ(n) over a frame, by solving the normal (Yule–Walker) equations with the Levinson–Durbin algorithm. ```text Encoder (transmitter) speech -> [A/D] -> [frame 20 ms] -+-> [LPC analysis: | a1..ap, gain G] +-> [pitch / V-UV detector] -> quantize & multiplex -> bit stream Decoder (receiver) [pulse train @ pitch]--+ +-[V/UV switch]-(×G)-+ [white noise gen.]-----+ | v speech <- [D/A] <- [all-pole filter 1/A(z)] ``` **Operation** 1. Speech is sampled (8 kHz) and divided into frames of about 20 ms. 2. **LPC analysis** finds about 10 predictor coefficients (vocal-tract filter) and the gain *G* for each frame. 3. A **pitch detector** decides voiced/unvoiced and measures the pitch period. 4. Coefficients, gain, pitch and V/UV flag are quantized and transmitted; e.g. LPC-10 sends 54 bits per 22.5 ms frame = 2.4 kbps. 5. At the receiver, the excitation is a periodic **pulse train** (voiced) or **white noise** (unvoiced), scaled by *G*. 6. The excitation drives the **all-pole synthesis filter** H(z) = G / (1 − Σ aₖz⁻ᵏ) to rebuild speech. **Merits:** very low bit rate (2.4–4.8 kbps). **Drawback:** synthetic, "robotic" quality. Improved versions (multi-pulse, RELP, CELP, RPE-LTP in GSM) send a better excitation signal. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Where do most of the energy and intelligibility of telephone speech lie? A. 20 Hz to 20 kHz B. 300 to 3400 Hz C. 3.4 to 8 kHz D. 0 to 100 Hz Answer: B. Telephone-band speech occupies about 300-3400 Hz. (Key point: Speech bandwidth) 2. In LPC, how is each sample predicted? A. As a linear combination of the previous p samples B. From the next p samples C. As the average of the frame D. From the pitch only Answer: A. s^(n) = sum a_k s(n-k) over the previous p samples, with a_k minimising mean square error. (Key point: LPC prediction) 3. What does an LPC encoder transmit? A. The waveform samples B. Only the pitch C. Predictor coefficients, gain, pitch and voiced/unvoiced flag D. The residual at 64 kbps Answer: C. Only filter parameters, gain and excitation type are sent, not the waveform. (Key point: Transmitted parameters) 4. What excites the all-pole synthesis filter for voiced and unvoiced frames? A. Noise for voiced, pulses for unvoiced B. Pulse train at pitch for voiced, white noise for unvoiced C. Pulses for both D. Noise for both Answer: B. Voiced sounds are quasi-periodic so a pulse train is used; unvoiced sounds are noise-like. (Key point: Excitation at decoder) 5. What is the main drawback of basic LPC vocoders like LPC-10? A. High bit rate B. Needs training sequence C. Synthetic, robotic quality D. Cannot work with frames Answer: C. Basic LPC gives 2.4 kbps but synthetic quality; CELP and RPE-LTP improve the excitation. (Key point: LPC drawback) ## Related in Wireless Communication - [Speech characteristics in coder design](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-characteristics-coder-design) — Wireless Communication, chapter 6, asked 3× - [Characteristics of speech signal](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-characteristics) — Wireless Communication, chapter 6 - [Formant vocoder and speech characteristics](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aformant-vocoder-speech) — Wireless Communication, chapter 6 - [Channel coding and types of LPC](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Achannel-coding-lpc-types) — Wireless Communication, chapter 6 - [GSM signal processing (speech to radio)](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Agsm-signal-processing) — Wireless Communication, chapter 8, asked 2× - [Speech characteristics; formant and channel vocoder](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-formant-channel-vocoder) — Wireless Communication, chapter 6 ## Related in other subjects - [Frequency counter operation with block diagram](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Afrequency-counter) — Digital Logic, chapter 11, asked 14× - [Data logger block diagram and operation](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Adl-block) — Instrumentation II, chapter 5, asked 6× - [PID control operation with block diagram](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Apid-operation-block-diagram) — Embedded System, chapter 7, asked 4× - [T-S characteristics; why linear portion operation](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Ats-linear-portion-operation) — Electrical Machines, chapter 5