The WiFi Interface on the DSP-7 board has a separate ARM micro controller and a separate firmware. It uses the well known ESP-07S WLan interface.
This firmware can be updated using the following procedure:
Flashing new firmware is done via a serial interface. This serial interface work with 3,3v levels and is not a RS-232. A level converter RS232 <-> 3.3v is requred. These level converters are easily available from various computer stores for only little money. Look for a USB-serial interface with 3.3v levels.
see the 6-pin connector in this picture.
this connector has a ground and 3.3v pin to supply the level converter (if required). Some level converters use the PC's USB port for supply, in this case you need to connect only the ground pin. The other two pins are the serial input (RxD) and output (TxD)
Starting the bootloader:
switch OFF the board, then connect the PGM pins (see red mark in the picture), then switch ON the board.
The LED will be off and the WiFi Interface is waiting for new firmware via the serial interface.
Download the actual WiFi firmware HERE.
Flashing the firmware:
Flashing is done under Linux with the tool: esptool.py from https://github.com/espressif/esptool
(this tool is also available for Windows, I have not tested it under Windows).
Open a terminal and flash the firmware into the WiFi Interface using this command line:
esptool.py -p /dev/ttyUSB0 --baud 115200 write_flash 0 dsp7wifi_v100.bin