In this paper, the 1-D real-valued discrete Gabor transform (RDGT) proposed in our previous work and its relationship with the complex-valued discrete Gabor transform (CDGT) are briefly reviewed. Block time-recursive RDGT algorithms for the efficient and fast computation of the 1-D RDGT coefficients and for the fast reconstruction of the original signal from the coefficients are then developed in both the critical sampling case and the oversampling case. Unified parallel lattice structures for the implementation of the algorithms are studied. And the computational complexity analysis and comparison show that the proposed algorithms provide a more efficient and faster approach for the computation of the discrete Gabor transforms.

Phase-Locked Loop (PLL) designers have two major problems with regard to the production of practical, portable multimedia communication systems. The first is the difficulty of achieving both fast lock time and low jitter operation simultaneously. This can be particularly difficult because the increase in loop stability needed to reduce jitter increases the lock time. The second is the problem caused by circuits operating at low voltage supplies. Low voltage supplies adversely effect the performance of phase-frequency detectors and charge pump circuits, and they can decrease the noise immunity of oscillators. We have developed a hot-standby architecture, which can achieve both fast lock time and low jitter operation simultaneously, and low-voltage circuit techniques, such as a noise-immune adaptive-gain voltage-controlled oscillator, for a fabricated PLL. This PLL is fully integrated onto a 480-µm450-µm die area with 0.18-µm CMOS technology. It can operate from 0.5 V to 1.2 V, and with a lock range from 40 MHz to 170 MHz at 0.5 V. The jitter is less than 200 ps and the lock time is less than 500 ns.

A 3.2 GHz, 50 mW, 1 V, GaAs clock pulse generator (CG) based on a phase-locked loop (PLL) circuit has been designed for use as an on-chip clock generator in future high speed processor LSIs. 0.5 µm GaAs MESFET and DCFL circuit technologies have been used for the CG, which consists of 224 MESFETs. An "enhanced charge-up current" inverter has been specially designed for a low power and high speed voltage controlled oscillator (VCO). In this new inverter, a voltage controlled dMESFET is combined in parallel with the load dMESFET of a conventional DCFL inverter. This voltage controlled dMESFET produces an additional charge-up current resulting in the new VCO obtaining a much higher oscillation frequency than that of a ring oscillator produced with a conventional inverter. With a single 1 V power supply (Vdd), SPICE calculation results showed that the VCO tuning range was 2.25 GHz to 3.65 GHz and that the average VCO gain was approximately 1.4 GHz/V in the range of a control voltage (Vc) from 0 to 1 V. Simulation also indicated that at a Vdd of 1 V the CG locked on a 50 MHz external clock and generated a 3.2 GHz internal clock (=50 MHz64). The jitter and power dissipation of the CG at 3.2 GHz oscillation and a Vdd of 1 V were less than 8.75 psec and 50 mW, respectively. The typical lock range was 2.90 GHz to 3.59 GHz which corresponded to a pull-in range of 45.3 MHz to 56.2 MHz.